Dynamical Systems Courses and Certifications

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
• Self-Paced
• 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
• Self-Paced
• Free Video

Simons Semester on Dynamics

Rigorous Computer Algorithms for Chaotic Dynamics - Lecture 1

Dive into rigorous computer algorithms for chaotic dynamics, exploring spectral radius computation and its applications in hyperbolic systems and parameter estimation.

• YouTube
• 1 hour 35 minutes
• Self-Paced
• Free Video

Simons Semester on Dynamics

When Topology Forces Dynamics - Lecture 1

Explore topological dynamics, focusing on how topology influences system behavior. Gain insights into fixed point index, Nielsen theory, and homotopy stability theorems.

• YouTube
• 1 hour 35 minutes
• Self-Paced
• Free Video

Simons Semester on Dynamics

Dynamical Approximations of Postsingularly Finite Entire Maps

Explore dynamical approximations of postsingularly finite entire maps, focusing on maps with finitely many singular values and their global dynamics. Discover connections between approximations, combinatorics, and Teichmuller spaces.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Simons Semester on Dynamics

Counting Periodic Orbits of One-Dimensional Maps - Lecture 2

Delve into the mathematics of counting periodic orbits in one-dimensional maps. Explore connections to number theory and thermodynamic formalism, focusing on interval and complex rational maps.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Simons Semester on Dynamics

Generalized Pseudo-Anosov Maps from Holomorphic Dynamics

Explore the connection between quadratic polynomial dynamics and surface homeomorphisms, focusing on generalized pseudo-Anosov extensions of Hubbard tree dynamics.

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

Simons Semester on Dynamics

Dynamical Complexity in the Rössler System

Uncover the analytical connection between Rössler equations and the logistic family. Explore periodic orbits, topologies, and complex dynamics in this mathematical exploration of chaotic attractors.

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

Simons Semester on Dynamics

Monotonicity of Entropy in Families of Interval Maps - Lecture 1

Explore the transfer operator, holomorphic motions, and entropy monotonicity in interval maps. Gain insights into applications in rational dynamics and quadratic families.

• YouTube
• 1 hour 28 minutes
• Self-Paced
• Free Video

Simons Semester on Dynamics

Equilibrium States Through Potential Theory - Lecture 2

Dive into equilibrium states for rational maps and endomorphisms, exploring their construction through potential theory and their statistical properties in thermodynamic formalism.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

Stony Brook Mathematics

Spontaneous Stochasticity in Multi-Scale Dynamics

Explore spontaneous stochasticity in multi-scale dynamics, focusing on turbulence models and the formalization of stochastic solutions using renormalization-group operator attractors.

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

BIMSA

Dynamics of BCZ Cocycles and the Riemann Hypothesis

Explore the BCZ map's connection to Farey fractions, horocycle flow, and the Riemann Hypothesis. Gain insights into recent developments in BCZ cocycles and their dynamical implications.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video