Nonlinear Dynamics and Chaos
Explore nonlinear dynamics and chaos through analytical methods, examples, and applications in physics, biology, and engineering. Develop mathematical theory and gain insights into complex systems behavior.
Mandelbrot, 1/f Noise, and The Mind's Eye in Complexity Science
Exploring Mandelbrot's contributions to 1/f noise, long-range dependence, and fractional models. Discusses the impact of cognitive diversity on scientific progress and the importance of visual thinking in mathematics.
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…
The Julia Sets of Chebyshev's Method with Small Degrees
Explore the dynamics of Chebyshev's method applied to cubic polynomials. Investigate Julia sets, connectivity conditions, and parametrization of rational maps in this mathematical deep dive.
Gauss-Lucas Theorem in Polynomial Dynamics
Dive into the Gauss-Lucas theorem's applications in polynomial dynamics, exploring convex hulls of Julia sets and their preimages for complex polynomials.
Monotonicity of Entropy in Families of Interval Maps - Lecture 2
Explore the transfer operator, holomorphic motions, and entropy monotonicity in interval maps. Gain insights into applications in rational dynamics and quadratic families.
Monotonicity of Entropy in Families of Interval Maps - Lecture 1
Explore the transfer operator, holomorphic motions, and entropy monotonicity in interval maps. Gain insights into applications in rational dynamics and quadratic families.
Beyond the Mandelbrot Set - An Intro to Holomorphic Dynamics
Explore holomorphic dynamics, iterative complex functions, and fractals. Delve into Mandelbrot sets, fixed points, cycles, and Julia sets for a fascinating journey through mathematical visualization.
Newton's Method Produces This Fractal, Why Don't We Teach It in Calculus Classes?
Explore the fascinating fractal produced by Newton's method for finding roots of polynomials, revealing unexpected complexity in a seemingly simple mathematical technique.
Coding a 3D Fractal
Learn to visualize the 3D Mandelbulb fractal using Processing (Java). Explore triplex numbers, spherical coordinates, and point cloud rendering techniques to create stunning fractal visualizations.
Learn Rust Programming
Master Rust's key concepts: traits, enums, borrow checker, error handling, and iterators. Gain practical skills through code reviews, fractals, and StackOverflow's top questions.
Day Trading Fractals
Learn to use fractals for day trading and swing trading in forex, including market turns, breakouts, and trend line drawing techniques.
Fractals Are Typically Not Self-Similar
Explore fractal dimension, self-similarity, and scaling in this engaging explanation that challenges common misconceptions about fractals and their properties.
El punto ciego en el camino de la vida - Fractales y perseverancia en robótica espacial
Andrés Mora explora cómo los fractales y la perseverancia se aplican en robótica y navegación espacial, utilizando su experiencia en la NASA para ilustrar el manejo de desafíos en la vida y la tecnología.
Low-Dimensional Solenoidal Manifolds
Exploración de manifolds solenoidales de baja dimensión, sus propiedades topológicas y estructurales, y nuevos resultados en este campo de la geometría y topología.
Non-Almost Finite Actions on the Cantor Set - Amenable Wreath Products
Explore non-almost finite actions on the Cantor set by amenable wreath products, challenging Kerr's topological analogue of the Ornstein-Weiss theorem in measurable dynamics.
Holomorphic Movements in Complex Analysis - Lecture 1
Explorez les mouvements holomorphes et leur application aux ensembles de Julia. Découvrez le lambda-lemma et son impact sur les systèmes dynamiques complexes.
Mouvements Holomorphes: Variation of Properties in Holomorphic Motions - Lecture 2
Explorez la variation des ensembles de Julia en fonction des polynômes. Découvrez les mouvements holomorphes et leur impact sur le diamètre, la dimension, l'aire et la capacité des ensembles.
The Crossing Paths of Mandelbrot and Schützenberger - An Episode of Crossovers
Explore the intersecting trajectories of Mandelbrot and Schützenberger in discrete mathematics and computer science, uncovering fascinating crossovers in their work.
Fractional Gaussian and Stable Random Fields on Fractals
Explore fractional Gaussian and stable random fields on fractals, covering key concepts like covariance functions, stochastic integrals, and Laplace operators.
The Modular Mandelbrot Set
Explore the Modular Mandelbrot set with Luna Lomonaco in this IMPA 70th anniversary conference talk. Delve into advanced mathematical concepts and cutting-edge research in complex dynamics.