Simons Semester on Dynamics Courses

Rigidity and Ratner's Rigidity Theorem in Horocycle Flows - Lecture 5

Delve into the rigidity theory of horocycle flows, exploring Ratner's Rigidity Theorem and its implications for dynamical systems in hyperbolic geometry and ergodic theory.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Some Arguments in Equidistribution - Lecture 7

Delve into advanced concepts of ergodic theory, including measure preservation, Birkhoff's theorem, and ergodicity of flows on the 2-torus through mathematical proofs and key theorems.

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

Some Arguments in Equidistribution - Lecture 3

Delve into measure-preserving dynamics and ergodic theory, exploring Birkhoff's theorem, irrational circle rotations, and ergodicity concepts through detailed mathematical proofs and key theorems.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Introduction to KAM Theory - Lecture 2

Delve into the fundamentals of KAM theory and its application in celestial mechanics, exploring quasi-periodic motions, small divisors, and analytical circle diffeomorphisms in dynamical systems.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Time-Changes: Definitions, Basic Facts, Ergodicity and Mixing - Lecture 4

Delve into ergodic and mixing properties of horocycle flows, exploring time-changes, their parabolic behavior, and fascinating phenomena in dynamical systems and mathematical physics.

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

Mixing and Equidistribution in Horocycle Flows - Lecture 3

Delve into ergodic theory and mixing properties of horocycle flows, exploring their smooth time-changes, rigidity theorems, and applications beyond SL2(R) in dynamical systems.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Some Arguments in Equidistribution - Lecture 4

Delve into advanced concepts of ergodic theory, including measure preservation, Birkhoff's theorem, and ergodicity of flows on the 2-torus, with applications to hyperbolic automorphisms.

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

Introduction to KAM Theory - Lecture 1

Delve into the fundamentals of Kolmogorov-Arnold-Moser (KAM) theory, exploring quasi-periodic motions, celestial mechanics stability, and analytical solutions for circle diffeomorphisms and Hamiltonian systems.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

On the Dani Correspondence and Its Applications - Lecture 3

Delve into ergodic theory and dynamics applications in Diophantine approximation, exploring Dani's correspondence and its impact on understanding rational number density patterns.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 3

Delve into random matrix products theory, exploring stationary probability measures, Lyapunov exponents, and their applications in dynamical systems and ergodic theory through advanced mathematical concepts.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Ergodicity and Horocycle Ergodic Averages on Compact Spaces - Lecture 2

Delve into ergodic and mixing properties of horocycle flows, exploring their time-changes, asymptotics, and fundamental mathematical concepts in dynamical systems theory.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

On the Dani Correspondence and Its Applications - Lecture 2

Delve into Diophantine approximation through ergodic theory, exploring the Dani correspondence and its dynamic interpretation of rational number density in the real line.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 2

Delve into random matrix products theory, exploring stationary probability measures, Lyapunov exponents, and their applications in dynamical systems and ergodic theory through advanced mathematical concepts.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Some Arguments in Equidistribution - Lecture 3

Delve into advanced concepts of ergodic theory, including measure preservation, Birkhoff's theorem, and ergodicity of flows on the 2-torus, with applications to hyperbolic automorphisms.

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

Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 1

Delve into random matrix products theory, exploring Lyapunov exponents, stationary measures, and probability measures on projective space through dynamic systems and ergodic theory perspectives.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video