Introductory Non-Linear Dynamics
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…
Non-hyperbolic Measures of Maximally Possible Entropy in Transitive Dynamical Systems
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.
Strong Positive Recurrence for Diffeomorphisms
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.
Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 4
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.
Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 3
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.
Continuity Properties of Lyapunov Exponents - Lecture 5
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.
Continuity Properties of Lyapunov Exponents - Lecture 7
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.
Continuity Properties of Lyapunov Exponents for Smooth Surface Diffeomorphisms - Lectures 1 and 2
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.
Rigorous Computer Algorithms for Chaotic Dynamics - Lecture 1
Dive into rigorous computer algorithms for chaotic dynamics, exploring spectral radius computation and its applications in hyperbolic systems and parameter estimation.
Continuity Properties of Lyapunov Exponents - Lectures 3 and 4
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.
Rigorous Computer Algorithms for Chaotic Dynamics - Lecture 2
Dive into rigorous computer algorithms for chaotic dynamics, exploring transfer operators, spectral radius computation, and estimating key parameters in hyperbolic systems.
Chaotic Dynamical Systems
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.
Lyapunov Exponents for Small Random Perturbations - Alex Blumenthal
Explore Lyapunov exponents in random perturbations of hyperbolic 2D volume-preserving diffeomorphisms, including the Standard Map, with insights on asymptotic dynamics and invariant structures.
Dynamics of Smooth Chaotic Surface Diffeomorphisms - 34th CBM Plenary Lecture
Explore a palestra sobre dinâmica de difeomorfismos caóticos suaves em superfícies, apresentada por Omri Sarig no 34º Colóquio Brasileiro de Matemática.
Theoretical and Numerical Approach to Lyapunov Exponents of Skew-Product Semiflows
Explore Lyapunov exponents in skew-product semiflows through theoretical and numerical approaches, enhancing understanding of dynamical systems.
Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 3
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.
Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 2
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.
Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 1
Delve into random matrix products theory, exploring Lyapunov exponents, stationary measures, and probability measures on projective space through dynamic systems and ergodic theory perspectives.
One-Parameter Families of Hyperbolic Iterated Function Systems on the Line - Lecture 3
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.
Estimating Dimension and Lyapunov Exponents - Lecture 2A
Explore advanced mathematical concepts in dimension theory, including Hausdorff dimensions, Lyapunov exponents, and their applications to number theory and geometric systems.
Estimating Dimension and Lyapunov Exponents - Lecture 2B
Explore advanced mathematical concepts in dimension theory, including Hausdorff dimensions, Lyapunov exponents, and their applications to number theory and geometric systems.