Dynamical Systems Courses and Certifications

Simons Semester on Dynamics

Models for Dynamical Systems in Dimensions 1 and 2 - Lecture 2

Explore models for dynamical systems in 1D and 2D, focusing on Milnor-Thurston's theorem and its potential 2D analogue for surface diffeomorphisms.

• YouTube
• 1 hour 31 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

The Pruning Front Conjecture, Wandering Domains and Classification of Hénon Maps - Strange Attractors

Dive into topological dynamics of Hénon maps, exploring kneading theory, strange attractors, and wandering domains within the Wang-Young parameter set.

• YouTube
• 1 hour 49 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

Models for Dynamical Systems in Dimensions 1 and 2 - Lecture 1

Explore dynamical systems in 1D and 2D, focusing on Milnor-Thurston's theorem and its potential 2D analog for surface diffeomorphisms. Delve into connections with Teichmüller Theory and 3-manifold topology.

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

Robustly Transitive Endomorphisms and Strong Volume Expansion for Toral Endomorphisms

Dive into robust transitivity criteria for partially hyperbolic endomorphisms on the two-torus, exploring Blichfedt's theorem and its applications in dynamical systems.

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

Simons Semester on Dynamics

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.

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

Simons Semester on Dynamics

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.

• YouTube
• 1 hour 32 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

Structural Stability for Fibrewise Anosov Diffeomorphisms on Principal Torus Bundles

Explore structural stability for fibrewise Anosov diffeomorphisms on principal torus bundles, focusing on topological conjugacy and linear fiber mappings.

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

Simons Semester on Dynamics

Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 1

Dive into chain recurrence classes of generic diffeomorphisms, exploring advanced concepts in dynamical systems and topology.

• YouTube
• 1 hour 31 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

On Pseudoarc and Dynamics

Explore the fascinating world of pseudoarc, its topological significance, and its connections to dynamical systems in this insightful lecture by Piotr Oprocha.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

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.

• YouTube
• 1 hour 39 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

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.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

Measurable Pseudo-Anosovs in Surface Homeomorphisms

Explore the dynamics of measurable pseudo-Anosov homeomorphisms, their origins in inverse limits of tent maps, and their role in surface homeomorphism dynamics.

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

Simons Semester on Dynamics

When Topology Forces Dynamics - Lecture 2

Explore the interplay between topology and dynamics, uncovering how topological considerations reveal crucial insights into system behavior and stability under perturbations.

• YouTube
• 1 hour 28 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

Typical Properties of Lebesgue Measure-Preserving Circle Maps

Explore recent findings on typical dynamical properties of Lebesgue measure-preserving maps, focusing on circle cases. Gain insights into collaborative research on one-dimensional manifolds.

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

Simons Semester on Dynamics

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.

• YouTube
• 1 hour 33 minutes
• On-Demand
• Free Video