Dynamical Systems Courses and Certifications

Simons Semester on Dynamics

Infinite Renormalizability and Non-Uniform Partial Hyperbolicity in Two-Dimensional Dynamical Systems

Dive into the renormalization theory of dynamical systems, exploring its extension to two-dimensional settings and the concept of infinite renormalizability in diffeomorphisms.

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

Simons Semester on Dynamics

Strong Positive Recurrence for Diffeomorphisms

Explore strong positive recurrence in diffeomorphisms, its implications for entropy-maximizing measures, and its equivalence to Lyapunov exponent continuity. Gain insights into smooth diffeomorphisms on compact surfaces.

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

Simons Semester on Dynamics

Birkhoff Sums as Distributions in Dynamical Systems

Explore Birkhoff sums as distributions in dynamical systems, examining regularity results for hyperbolic systems and applications to deformation theory in one-dimensional dynamical systems.

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

Simons Semester on Dynamics

Methods for Studying Abelian Actions and Centralizers - Lecture 3

Explore two methods for studying abelian actions and centralizers: linearization and non-linearization. Delve into cohomology concepts and their applications in dynamical systems analysis.

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

Simons Semester on Dynamics

Dimension of Stationary Measures - Lecture 2

Explore the dimension of stationary measures in random walks, focusing on matrix group actions over flag spaces. Gain insights into exact dimensions, partial answers, and the intricate structure of flag spaces.

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

Simons Semester on Dynamics

Methods for Studying Abelian Actions and Centralizers - Lecture 6

Explore centralizer rigidity and classification in accessible examples of dynamical systems. Gain insights into the non-generic situations where smooth centralizers form larger groups, particularly in algebraic systems.

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

Simons Semester on Dynamics

Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 4

Delve into spectrum rigidity and joint integrability for Anosov systems on tori. Explore topological conjugacy of non-invertible Anosov maps on 2-torus and its implications for smooth conjugacy along stable foliations.

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

Simons Semester on Dynamics

Newhouse Phenomenon in the Complex Hénon Family

Explore the Newhouse phenomenon in complex Hénon maps, focusing on stable homoclinic tangencies and intersections between dynamical Cantor sets generated by conformal IFSs.

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

Simons Semester on Dynamics

Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 3

Delve into spectrum rigidity and joint integrability for Anosov systems on tori. Explore the equivalence between geometric rigidity and dynamical spectral rigidity in Anosov diffeomorphisms, focusing on irreducible cases with split stable bundles.

• YouTube
• 58 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

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

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

Simons Semester on Dynamics

Counting Periodic Orbits of One-Dimensional Maps - Lecture 3

Delve into the mathematics of counting periodic orbits in one-dimensional maps. Explore connections to number theory, thermodynamic formalism, and the prime orbit theorem for hyperbolic systems.

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