Dynamical Systems & Chaos Courses and Certifications

A Framework for Machine Learning of Model Error in Dynamical Systems

Explore a framework for machine learning to model error in dynamical systems, focusing on linear oscillators, partial information, and hybrid modeling techniques.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

From Undirected to Directed Networks of Dynamical Agents - Robin Delabays

Explore the impact of directedness in network models, focusing on diffusive interactions and their consequences in systems like power grids, brain networks, and social networks.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

The Statue in the Stone: How Dynamical Systems Discover Environmental Patterns

Explores how complex systems adapt to environmental patterns, favoring stable configurations that match external forces. Illustrates with toy models and swarm-robotics experiment.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Using Curvature to Understand the Structure of Dynamics

Explore curvature's role in understanding attractor dynamics and its application in time-series data reconstruction, focusing on optimal time-delay parameter selection for delay-coordinate embeddings.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Autocatalysis and Unstable Cores in Parameter-Rich Chemical Reaction Networks

Explore dynamic instability in chemical reaction networks, focusing on autocatalysis and unstable cores. Gain insights into parameter-rich systems and their implications for network behavior.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Homogeneous Dynamics - Part 2 - Lecture 21

Explore quantitative Ratner theorems through Lindenstrauss-Mohammadi's work and discover how projection theory contributes to advanced homogeneous dynamics proofs.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Homogeneous Dynamics - Part 1 - Lecture 20

Explore homogeneous dynamics through projection theory in this MIT mathematics lecture covering fundamental concepts and applications.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Fields Institute

Residual Dynamic Mode Decomposition- Rigorous Data-Driven Computation of Spectral Properties of Koopman Operators for Dynamical Systems

Explore rigorous data-driven methods for computing spectral properties of Koopman operators in dynamical systems, focusing on Residual Dynamic Mode Decomposition and its applications.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Fields Institute

About Dulac's Problem in R3 for Perturbations of Linear Non-Degenerated Centers

Explora el problema de Dulac en R^3 para perturbaciones de centros lineales no degenerados, analizando mapas de retorno, conjuntos de ciclos y técnicas de explosión para sistemas dinámicos.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Fields Institute

Hilbert's 16th Problem and O-Minimality - Lecture 1

Explore the topology of cycles, limit cycles, and related mathematical concepts in this advanced graduate-level lecture on Hilbert's 16th problem and o-minimality.

• YouTube
• 1 hour 43 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Introduction to Dynamical Systems - Lecture 2

Explore non-smooth dynamical systems, bifurcations, and complex networks. Learn about border collision, switched systems, and applications in engineering and natural phenomena.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Taylor McAdam- Almost-Prime Times in Horospherical Flows

Explore effective results in horospherical flows, their applications to number theory, and connections to Sarnak's Mobius disjointness conjecture in this advanced mathematics lecture.

• YouTube
• 42 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

The Dynamical Systems Approach to Spatially Homogenous Einstein-Vlasov Cosmology

Explore spatially homogenous Einstein-Vlasov cosmology using dynamical systems analysis. Investigate asymptotic solutions near singularities and expanding futures, focusing on Kantowski-Sachs models with Vlasov matter.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Dynamics of Smooth Surface Diffeomorphisms - Spectral Gap and Stochastic Properties

Explore surface diffeomorphisms, spectral gaps, and stochastic properties in smooth dynamics. Gain insights into symbolic models, entropy continuity, and hyperbolic systems.

• YouTube
• 1 hour 23 minutes
• Self-Paced
• Free Video

ICTP Mathematics

SRB Measures and Young Towers - Lecture 3 of 4

Explore SRB measures and Young towers in dynamical systems, focusing on nonuniformly hyperbolic systems and their statistical properties. Learn about recent advances in this field of mathematics.

• YouTube
• 1 hour 54 minutes
• Self-Paced
• Free Video