Simons Semester on Dynamics Courses

Prediction of Dynamical Systems from Time-Delayed Measurements with Self-Intersections

Explore new versions of Takens time-delay embedding theorem for predicting dynamical systems from one-dimensional measurements, including deterministic and probabilistic settings with error decay rates.

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

Markovian Families in the Bifoliated Plane of Anosov Flows in Dimension 3

Explore a 31-minute lecture on Markovian families in the bifoliated plane of Anosov flows in three dimensions. Delve into a novel approach for classifying transitive Anosov flows on 3-manifolds up to orbital equivalence. Learn about the generalization of…

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

Christian Bonatti (Université de Bourgogne / CNRS), lecture 2

Explore the intricacies of chain recurrence classes in generic diffeomorphisms through this comprehensive lecture delivered by Christian Bonatti from Université de Bourgogne / CNRS. Delve into advanced mathematical concepts and theories as part of the Si…

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

Maria José Pacifico (Universidade Federal do Rio de Janeiro)

Explore the fascinating world of Lorenz attractors in this 52-minute lecture by Maria José Pacifico from the Universidade Federal do Rio de Janeiro. Delve into the history and significance of Lorenz attractors since their discovery in 1963, examining the…

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

Continuity Properties of Lyapunov Exponents - Lectures 8 and 9

Explore the continuity properties of Lyapunov exponents in two lectures from the Simons Semester on Dynamics. Delve into the control of Lyapunov exponents using entropy for smooth surface diffeomorphisms, based on recent joint works with Sylvain Crovisie…

• YouTube
• 1 hour 38 minutes
• On-Demand
• Free Video

Entropy and Gibbs Measures for Hyperbolic Systems - Lecture 2

Explore the intricacies of entropy and Gibbs measures for hyperbolic systems in this comprehensive lecture by Mark Pollicott from the University of Warwick. Delve into classical examples of hyperbolic systems, including toral automorphisms and geodesic f…

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

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

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

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

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

On the Algebraic Structure of Groups of Area-Preserving Homeomorphisms - Lecture 1

Explore the algebraic structure of area-preserving homeomorphism groups, focusing on Fathi's question and the simplicity conjecture for compact surfaces. Gain insights into link spectral invariants and their role in solving this problem.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

When Topology Forces Dynamics - Lecture 4

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

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

When Topology Forces Dynamics - Lecture 3

Explore the intersection of topology and dynamics in this lecture titled "When topology forces dynamics." Delve into scenarios where topological considerations, such as actions on homology or the fundamental group, significantly influence a system's dyna…

• YouTube
• 1 hour 26 minutes
• On-Demand
• Free Video

A Spectral Gap for the Transfer Operator on Complex Projective Spaces - Lecture 4

Explore the transfer operator on complex projective spaces, focusing on spectral gaps, equilibrium states, and statistical properties in holomorphic dynamics. Gain insights into pluripotential theory applications.

• YouTube
• 1 hour 36 minutes
• On-Demand
• Free Video

Counting Periodic Orbits of One-Dimensional Maps - Lecture 1

Dive into the fascinating world of periodic orbits in one-dimensional maps. Explore connections to number theory and thermodynamic formalism, starting with Milnor and Thurston's work on interval maps.

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