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#Lyapunov Exponents

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NPTEL

Introductory Non-Linear Dynamics

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This course is designed to introduce students to the basic ideas of Dynamical systems, Stability, and chaos, largely using Iterative mappings as the model. The course will focus on qualitative ideas and will require students to explore dynamics through s…
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13 Lesons
6 hours
On-Demand
Free-Video
Simons Semester on Dynamics

Non-hyperbolic Measures of Maximally Possible Entropy in Transitive Dynamical Systems

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Explore the dynamics of nonhyperbolic partially hyperbolic diffeomorphisms, focusing on skew products of circle diffeomorphisms and their implications for ergodic measures and entropy in dynamical systems.
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1 Lesons
52 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Strong Positive Recurrence for Diffeomorphisms

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Explore strong positive recurrence in diffeomorphisms, its implications for entropy-maximizing measures, and its equivalence to Lyapunov exponent continuity. Gain insights into smooth diffeomorphisms on compact surfaces.
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1 Lesons
58 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 4

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Delve into spectrum rigidity and joint integrability for Anosov systems on tori. Explore topological conjugacy of non-invertible Anosov maps on 2-torus and its implications for smooth conjugacy along stable foliations.
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1 Lesons
56 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 3

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Delve into spectrum rigidity and joint integrability for Anosov systems on tori. Explore the equivalence between geometric rigidity and dynamical spectral rigidity in Anosov diffeomorphisms, focusing on irreducible cases with split stable bundles.
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1 Lesons
58 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Continuity Properties of Lyapunov Exponents - Lecture 5

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Explore the control of Lyapunov exponents using entropy in smooth surface diffeomorphisms. Gain insights into recent research on expansion of smooth unstable curves and their relation to homoclinic tangencies.
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1 Lesons
59 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Continuity Properties of Lyapunov Exponents - Lecture 7

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Explore the control of Lyapunov exponents using entropy in smooth surface diffeomorphisms. Gain insights into recent research on expansion of smooth unstable curves and their relation to homoclinic tangencies.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Continuity Properties of Lyapunov Exponents for Smooth Surface Diffeomorphisms - Lectures 1 and 2

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Explore continuity properties of Lyapunov exponents in smooth surface diffeomorphisms. Gain insights into entropy control and its relation to expansion of smooth unstable curves and homoclinic tangencies.
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10 Lesons
1 hour 33 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Rigorous Computer Algorithms for Chaotic Dynamics - Lecture 1

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Dive into rigorous computer algorithms for chaotic dynamics, exploring spectral radius computation and its applications in hyperbolic systems and parameter estimation.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Continuity Properties of Lyapunov Exponents - Lectures 3 and 4

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Delve into the continuity properties of Lyapunov exponents in smooth surface diffeomorphisms, exploring entropy control and the impact of near homoclinic tangencies on unstable curve expansion.
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1 Lesons
1 hour 39 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Rigorous Computer Algorithms for Chaotic Dynamics - Lecture 2

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Dive into rigorous computer algorithms for chaotic dynamics, exploring transfer operators, spectral radius computation, and estimating key parameters in hyperbolic systems.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
Steve Brunton

Chaotic Dynamical Systems

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Explore chaotic dynamical systems, their sensitive dependence on initial conditions, and applications in nature and engineering. Learn to recognize chaos and numerically integrate these complex systems.
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7 Lesons
44 minutes
On-Demand
Free-Video
Institute for Advanced Study

Lyapunov Exponents for Small Random Perturbations - Alex Blumenthal

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Explore Lyapunov exponents in random perturbations of hyperbolic 2D volume-preserving diffeomorphisms, including the Standard Map, with insights on asymptotic dynamics and invariant structures.
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13 Lesons
1 hour
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Dynamics of Smooth Chaotic Surface Diffeomorphisms - 34th CBM Plenary Lecture

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Explore a palestra sobre dinâmica de difeomorfismos caóticos suaves em superfícies, apresentada por Omri Sarig no 34º Colóquio Brasileiro de Matemática.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Banach Center

Theoretical and Numerical Approach to Lyapunov Exponents of Skew-Product Semiflows

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Explore Lyapunov exponents in skew-product semiflows through theoretical and numerical approaches, enhancing understanding of dynamical systems.
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1 Lesons
25 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 3

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Delve into random matrix products theory, exploring stationary probability measures, Lyapunov exponents, and their applications in dynamical systems and ergodic theory through advanced mathematical concepts.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 2

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Delve into random matrix products theory, exploring stationary probability measures, Lyapunov exponents, and their applications in dynamical systems and ergodic theory through advanced mathematical concepts.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Simons Semester on Dynamics

Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 1

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Delve into random matrix products theory, exploring Lyapunov exponents, stationary measures, and probability measures on projective space through dynamic systems and ergodic theory perspectives.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

One-Parameter Families of Hyperbolic Iterated Function Systems on the Line - Lecture 3

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Delve into hyperbolic iterated function systems and their dimensional properties, exploring transversality methods for analyzing one-parameter families and their applications in measure theory and dynamics.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Estimating Dimension and Lyapunov Exponents - Lecture 2A

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Explore advanced mathematical concepts in dimension theory, including Hausdorff dimensions, Lyapunov exponents, and their applications to number theory and geometric systems.
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1 Lesons
51 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Estimating Dimension and Lyapunov Exponents - Lecture 2B

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Explore advanced mathematical concepts in dimension theory, including Hausdorff dimensions, Lyapunov exponents, and their applications to number theory and geometric systems.
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1 Lesons
44 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Estimating Dimension and Lyapunov Exponents - Lecture 1B

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Delve into advanced mathematical concepts exploring Hausdorff dimensions, Lyapunov exponents, and their applications to number theory and geometric systems through conformal iterated function schemes.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Estimating Dimension and Lyapunov Exponents - Lecture 1A

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Explore advanced mathematical concepts of Hausdorff dimension, Lyapunov exponents, and their applications in dynamical systems and number theory through detailed theoretical analysis.
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6 Lesons
37 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Lyapunov Exponents, From the 1960's to the 2020's by Marcelo Viana

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Explore the evolution of Lyapunov exponents in mathematics, from foundational concepts to recent developments, applications in smooth dynamics, and future directions in this comprehensive lecture.
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44 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Non-Asymptotic Results for Singular Values of Gaussian Matrix Products

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Explore non-asymptotic results for singular values of Gaussian matrix products, including convergence rates and Lyapunov exponent normality, based on joint research with Boris Hanin.
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10 Lesons
39 minutes
On-Demand
Free-Video
International Mathematical Union

Lower Bounds on the Top Lyapunov Exponent of Stochastic Systems

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Explore lower bounds on top Lyapunov exponents in stochastic systems, examining mathematical techniques and implications for understanding system behavior and stability.
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1 Lesons
49 minutes
On-Demand
Free-Video
ICTP Mathematics

Partially Hyperbolic Diffeomorphisms - Lecture 9

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Explore advanced concepts in dynamical systems, focusing on partially hyperbolic diffeomorphisms and their properties in this in-depth mathematical lecture.
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1 Lesons
53 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 17

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Explore advanced concepts in dynamical systems theory, focusing on complex mathematical principles and their applications in modeling real-world phenomena.
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1 Lesons
1 hour 25 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 15

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Explore advanced concepts in dynamical systems theory, focusing on complex mathematical principles and their applications in modeling and analyzing evolving systems over time.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 12

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Explore advanced concepts in dynamical systems theory, focusing on complex mathematical principles and their applications in modeling and analyzing dynamic phenomena.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 10

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Explore advanced concepts in dynamical systems theory, focusing on complex mathematical principles and their applications in modeling real-world phenomena.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 8

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Explore advanced concepts in dynamical systems theory, focusing on complex mathematical principles and their applications in modeling real-world phenomena.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 02

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Explore advanced concepts in dynamical systems theory, focusing on mathematical principles and applications in complex systems analysis and modeling.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 03

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Explore advanced concepts in dynamical systems theory, focusing on mathematical principles and applications in complex systems analysis and modeling.
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1 Lesons
1 hour 27 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 04

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Explore advanced concepts in dynamical systems theory, focusing on mathematical principles and applications in complex systems analysis and modeling.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
ICTP Mathematics

Ergodicity in Smooth Dynamics - Lecture 10

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Explore ergodicity in smooth dynamics with Jana Rodriguez-Hertz, delving into advanced mathematical concepts and their applications in dynamical systems.
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1 Lesons
34 minutes
On-Demand
Free-Video
ICTP Mathematics

Ergodicity in Smooth Dynamics - Lecture 9

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Explore ergodicity in smooth dynamics with expert Amie Wilkinson, delving into advanced mathematical concepts and their applications in dynamical systems.
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1 Lesons
57 minutes
On-Demand
Free-Video
ICTP Mathematics

Ergodicity in Smooth Dynamics - Lecture 7

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Explore ergodicity in smooth dynamics with experts Rodriguez-Hertz and Wilkinson, delving into advanced concepts and applications in this comprehensive lecture.
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1 Lesons
53 minutes
On-Demand
Free-Video
ICTP Mathematics

Ergodicity in Smooth Dynamics - Lecture 5

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Explore ergodicity in smooth dynamics with experts Rodriguez-Hertz and Wilkinson, delving into advanced concepts and applications in this comprehensive lecture.
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1 Lesons
56 minutes
On-Demand
Free-Video
ICTP Mathematics

Ergodicity in Smooth Dynamics - Lecture 4

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Explore ergodicity in smooth dynamics with expert Amie Wilkinson, delving into advanced mathematical concepts and their applications in dynamical systems.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
ICTP Mathematics

Ergodicity in Smooth Dynamics - Lecture 3

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Explore ergodicity in smooth dynamics, delving into advanced concepts and applications in dynamical systems theory.
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1 Lesons
39 minutes
On-Demand
Free-Video
ICTP Mathematics

Ergodicity in Smooth Dynamics - Lecture 2

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Explore advanced concepts in ergodic theory and smooth dynamical systems, focusing on measure-preserving transformations and their properties in continuous-time systems.
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1 Lesons
41 minutes
On-Demand
Free-Video
ICTP Mathematics

Piecewise Expanding Maps of the Circle - Lecture 5

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Explore piecewise expanding maps on the circle, delving into advanced mathematical concepts and their applications in dynamical systems theory.
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1 Lesons
46 minutes
On-Demand
Free-Video
ICTP Mathematics

Piecewise Expanding Maps of the Circle - Lecture 4

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Explore piecewise expanding maps on the circle, delving into advanced mathematical concepts and their applications in dynamical systems theory.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
ICTP Mathematics

Piecewise Expanding Maps of the Circle - Lecture 3

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Explore piecewise expanding maps of the circle, delving into advanced mathematical concepts and their applications in dynamical systems theory.
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1 Lesons
48 minutes
On-Demand
Free-Video
ICTP Mathematics

Piecewise Expanding Maps of the Circle - Lecture 2

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Explore advanced concepts of piecewise expanding maps on the circle, building on previous knowledge and delving into more complex mathematical theories and applications.
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1 Lesons
46 minutes
On-Demand
Free-Video
Alan Turing Institute

Machine Learning Analysis of Chaos and Vice Versa - Edward Ott, University of Maryland

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Exploring machine learning's effectiveness in analyzing chaotic systems and vice versa. Covers short-term forecasting, ergodic properties, Lyapunov exponents, and the interplay between chaos theory and ML in understanding complex dynamical systems.
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16 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC)

Maximum Lyapunov Exponent for Temporal Networks

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Explore the Maximum Lyapunov Exponent concept in temporal networks, delving into complex systems analysis and network dynamics.
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1 Lesons
48 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Basics on Measure Rigidity

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Explorez les fondements de la rigidité des mesures avec Aaron Brown, abordant les concepts clés et leurs applications en mathématiques avancées.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
ICTP Condensed Matter and Statistical Physics

Dynamics Close to Equilibrium and Chaos - Lecture 3

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Explore equilibrium dynamics and chaos, delving into advanced concepts with expert insights from Anatoly Polkovnikov of Boston University.
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1 Lesons
1 hour 41 minutes
On-Demand
Free-Video
ICTP Condensed Matter and Statistical Physics

Dynamics Close to Equilibrium and Chaos - Lecture 2

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Explore equilibrium dynamics and chaos, delving into advanced concepts with insights from Boston University expert Anatoly Polkovnikov.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Regularity of the Lyapunov Exponents of Random SL(2,R)-Cocycles

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Explore regularity of Lyapunov exponents in random SL(2,R)-cocycles. Delve into advanced dynamical systems theory with expert Pedro Duarte at IMPA's international conference.
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1 Lesons
53 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Stability of the Lyapunov Exponents Under Random Noise

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Explore stability of Lyapunov exponents under random noise in dynamical systems. Gain insights from expert Silvius Klein at this international mathematics conference celebrating Marcelo Viana's 60th birthday.
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1 Lesons
49 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Continuity of Center Lyapunov Exponents in Interval Exchange Transformations

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Explore continuity of center Lyapunov exponents in interval exchange transformations with Karina Marín. Part of a broad dynamical systems conference celebrating Marcelo Viana's 60th birthday at IMPA.
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1 Lesons
35 minutes
On-Demand
Free-Video
Big Ideas In Dynamics

Pathological Foliations and Negative Central Lyapunov Exponents - Proof of the Lemma

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Explore negative central Lyapunov exponents, pathological foliations, and a key lemma proof in dynamical systems theory.
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1 Lesons
27 minutes
On-Demand
Free-Video
Banach Center

Constructing Periodic Boundary Points Through Pesin's Theory

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Explore Pesin's theory to construct periodic boundary points, delving into advanced mathematical concepts and applications.
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1 Lesons
52 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

One-Parameter Families of Hyperbolic Iterated Function Systems on the Line - Lecture 2B

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Delve into hyperbolic iterated function systems and their dimensional properties, exploring transversality methods for analyzing one-parameter families and their geometric characteristics.
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1 Lesons
47 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

One-Parameter Families of Hyperbolic Iterated Function Systems on the Line - Lecture 2A

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Delve into hyperbolic iterated function systems and their dimensional properties, exploring transversality methods for analyzing one-parameter families and their geometric characteristics in mathematical dynamics.
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1 Lesons
45 minutes
On-Demand
Free-Video
ICTP Mathematics

Diffusion of Wind-Tree Billiards and Lyapunov Exponents of the Hodge - Anton Zorich

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Explore wind-tree billiards diffusion and Hodge Lyapunov exponents in this advanced mathematics lecture by Anton Zorich, delving into complex dynamical systems and geometric analysis.
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1 Lesons
50 minutes
On-Demand
Free-Video
ICTP Mathematics

Symbolic Dynamics for Orbits with 0 Lyapunov Exponents - ICTP 2021

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Explore symbolic dynamics for orbits with zero Lyapunov exponents, covering key concepts like spacing reduction, temperability, and the greedy algorithm.
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14 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Cambridge Materials

Information Scrambling: A Path-Integral Perspective

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Explore quantum information scrambling, its quantification through Lyapunov exponents, and the role of path integrals in understanding universal bounds on chaos in thermal quantum systems.
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8 Lesons
22 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Lyapunov Exponents of the Navier-Stokes Equations

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Explore Lyapunov exponents in Navier-Stokes equations through Alex Blumenthal's conference talk, delving into probabilistic techniques for random and time-dependent dynamical systems.
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1 Lesons
51 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Quantum Bounds and Fluctuation-Dissipation Relation

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Explore quantum bounds for transport coefficients and their connection to the Fluctuation-Dissipation relation, with insights from high-energy physics and String Theory.
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1 Lesons
39 minutes
On-Demand
Free-Video
PCS Institute for Basic Science

The Complexity of Bohmian Positron Dynamics Inside a Chiral Carbon Nanotube

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Explore Bohmian positron dynamics in chiral carbon nanotubes, analyzing classical and quantum treatments, phase singularities, and complex trajectory behaviors.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
ICTP Condensed Matter and Statistical Physics

Dynamics Close to Equilibrium and Chaos - Lecture 1

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Explore fundamental concepts of dynamics near equilibrium and chaos, delving into theoretical frameworks and applications in condensed matter physics.
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1 Lesons
1 hour 39 minutes
On-Demand
Free-Video