Simons Semester on Dynamics Courses

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

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

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

On the Algebraic Structure of Groups of Area-Preserving Homeomorphisms - Lecture 3

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

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

Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 2

Explore the global rigidity properties of irreducible Anosov diffeomorphisms on T^d satisfying center bunching conditions in this advanced mathematics lecture. Delve into how joint integrability of strong stable and full unstable subbundles leads to dyna…

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

Collapsed Anosov Flows - Lectures 3 and 4

Explore partially hyperbolic systems and collapsed Anosov flows in dynamical systems. Gain insights into accessibility, ergodicity, and self-orbit equivalences of Anosov flows in 3-manifolds.

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

On the Algebraic Structure of Groups of Area-Preserving Homeomorphisms - Lecture 2

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

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Nicolas Gourmelon (Université de Bordeaux)

Explore a lecture on total renormalizations of perturbations of identity presented by Nicolas Gourmelon from Université de Bordeaux as part of the Simons Semester on Dynamics. Delve into the concept of total renormalization, defined as a transformation F…

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Rose Elliott Smith (University of Chicago)

Explore a 28-minute lecture on uniformly expanding random walks on manifolds, presented by Rose Elliott Smith from the University of Chicago as part of the Simons Semester on Dynamics. Delve into the dynamical property of uniform expansion, which indicat…

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

Salvador Zanata (Ime Usp)

Syllabus: Salvador Zanata (Ime Usp)

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

Collapsed Anosov Flows: Characterizations and Proofs - Lecture 2

Delve into equivalent characterizations of collapsed Anosov flows and their strong variants, exploring key mathematical proofs and theoretical foundations in dynamical systems.

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

Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 1

Explore the spectrum rigidity and joint integrability of Anosov systems on tori in this lecture from the Simons Semester on Dynamics. Delve into the strong rigidity properties arising from joint integrability in Anosov diffeomorphisms on tori, focusing o…

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

Smooth Models for Certain Partially Hyperbolic Systems

Explore a 21-minute lecture on smooth models for certain partially hyperbolic systems, presented by Margaret Doucette from the University of Chicago as part of the Simons Semester on Dynamics. Delve into the proof that fibered partially hyperbolic system…

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

Collapsed Anosov Flows - Lecture 1: Basic Definitions and Main Results

Explore the concept of collapsed Anosov flows in this first lecture of a mini-course on partially hyperbolic systems. Delve into basic definitions and the characterization of collapsed Anosov flows, including stronger variants. Examine examples and key r…

• YouTube
• 52 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