Dynamical Systems Courses and Certifications

Fields Institute

Deep Learning for Nonlinear Stability Analysis in Dynamical Systems

Explore deep learning techniques for analyzing nonlinear stability in dynamical systems, presented by Bogdan Epureanu from the University of Michigan.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Fields Institute

Koopman Operator Theory Based Machine Learning of Dynamical Systems

Explore advanced machine learning techniques for dynamical systems using Koopman operator theory, presented by Igor Mezic from UC Santa Barbara.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Fields Institute

Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces

Explore Koopman operator regression in reproducing kernel Hilbert spaces for dynamical systems, enhancing understanding of machine learning applications in complex systems analysis.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Fields Institute

Toward a Unification of Infinities

Explore the concept of unifying different types of infinities in mathematics, delving into advanced theoretical frameworks and their implications for transseries and dynamical systems.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Fields Institute

Rigidity of Saddle Loops

Explore the mathematical concept of rigidity in saddle loops, focusing on their properties and applications in dynamical systems theory.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Fields Institute

Holomorphic Continuation of R_an,exp - Germs: The Missing Lecture

Explore holomorphic continuation of R_an,exp-germs in this advanced mathematics lecture, delving into complex analysis and dynamical systems.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Fields Institute

Smooth Dynamic vs Symbolic Dynamic

Explore the interplay between smooth and symbolic dynamics in this advanced mathematics lecture by Olivier Mathieu, delving into complex theoretical concepts and their applications.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

ICTP Mathematics

SRB Measures and Young Towers - Lecture 4

Explore advanced techniques in dynamical systems, focusing on SRB measures and Young Towers. Learn about recent developments and applications in nonuniformly hyperbolic systems.

• YouTube
• 2 hours 23 minutes
• On-Demand
• Free Video

ICTP Mathematics

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 5

Explore advanced techniques in symbolic dynamics for complex hyperbolic systems. Gain insights into infinite Markov partitions and their applications in studying statistical properties of dynamical systems.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

ICTP Mathematics

SRB Measures and Young Towers - Lecture 2 of 4

Explore SRB measures and Young Towers in nonuniformly hyperbolic systems. Learn advanced techniques for studying statistical properties of complex dynamical systems.

• YouTube
• 1 hour 51 minutes
• On-Demand
• Free Video

ICTP Mathematics

SRB Measures and Young Towers - Lecture 1

Explore groundbreaking techniques in Ergodic Theory applied to differentiable dynamical systems. Learn about SRB measures, Markov Partitions, and Young Towers in nonuniformly hyperbolic systems.

• YouTube
• 2 hours 7 minutes
• On-Demand
• Free Video

ICTP Mathematics

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 1 of 5

Explore symbolic dynamics for nonuniformly hyperbolic systems, focusing on Markov Partitions and Young Towers. Learn advanced techniques to analyze complex dynamical systems and their statistical properties.

• YouTube
• 2 hours 6 minutes
• On-Demand
• Free Video

ICTP Mathematics

Dynamics of the Geodesic Flow on Surfaces Without Conjugate Points - Lecture 4

Explore geodesic flow dynamics on surfaces without conjugate points, focusing on uniqueness and ergodicity of maximal entropy measure and mixing properties of the flow.

• YouTube
• 1 hour 55 minutes
• On-Demand
• Free Video

ICTP Mathematics

Dynamics of the Geodesic Flow on Surfaces Without Conjugate Points - Lecture 2

Explore geodesic flow dynamics, maximal entropy measures, and Patterson-Sullivan measures on ideal boundaries in surfaces without conjugate points.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

ICTP Mathematics

Mating Quadratic Maps with the Modular Group

Explore holomorphic correspondences and their dynamics, focusing on a specific family of (2:2) correspondences and their relationship to the modular group and rational maps.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video