Lyapunov Exponents Courses and Certifications

Simons Semester on Dynamics

Estimating Dimension and Lyapunov Exponents - Lecture 1A

Explore advanced mathematical concepts of Hausdorff dimension, Lyapunov exponents, and their applications in dynamical systems and number theory through detailed theoretical analysis.

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

Simons Semester on Dynamics

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

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

Continuity Properties of Lyapunov Exponents - Lectures 3 and 4

Delve into the continuity properties of Lyapunov exponents in smooth surface diffeomorphisms, exploring entropy control and the impact of near homoclinic tangencies on unstable curve expansion.

• YouTube
• 1 hour 39 minutes
• On-Demand
• 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
• On-Demand
• Free Video

Big Ideas In Dynamics

Pathological Foliations and Negative Central Lyapunov Exponents - Proof of the Lemma

Explore negative central Lyapunov exponents, pathological foliations, and a key lemma proof in dynamical systems theory.

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

IMSA

Partially Hyperbolic Dynamics - Introduction to Rigidity and Lyapunov Exponents

Delve into the fascinating world of partially hyperbolic dynamics, exploring key concepts from Smale and Anosov to modern developments in dynamical systems and their structural stability.

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

Institute for Advanced Study

Lower Bounds on Lyapunov Exponents for Linear PDEs Driven by Stochastic Navier-Stokes

Explore lower bounds on Lyapunov exponents for linear PDEs driven by stochastic Navier-Stokes equations, including quantitative estimates and implications for fluid dynamics mixing phenomena.

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

Institute for Advanced Study

Lyapunov Exponents and Mixing in DiPerna-Lions Flows

Explore Lyapunov exponents and mixing in DiPerna-Lions flows, examining Bressan's conjecture and new results on asymptotic validity for time-periodic velocity fields.

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

Steve Brunton

Lagrangian Coherent Structures in Unsteady Fluids with Finite Time Lyapunov Exponents

Explore Lagrangian Coherent Structures and Finite Time Lyapunov Exponents in fluid dynamics. Learn about material lines, particle advection, and applications in aerodynamics, ocean mixing, and jellyfish feeding.

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

A Visual Approach to Nonlinear Dynamics

Discover how simple rules create complex behaviors through animated visuals exploring fixed points, bifurcations, chaos, and strange attractors in physical and biological systems.

• Complexity Explorer
• On-Demand
• Free Online Course

Institute for Advanced Study

Analysis and Mathematical Physics

Explore advanced mathematical physics through expert lectures on quantum systems, fluid dynamics, spectral theory, geometric analysis, and cutting-edge research from leading mathematicians and physicists.

• YouTube
• 3 days 8 hours 42 minutes
• On-Demand
• Free Video

Complexity Explorer

Nonlinear Dynamics - Introduction to Chaos Theory and Complex Systems

Explore chaotic systems, bifurcations, attractors, and fractal dimensions through mathematical modeling, ODE solving, and time series analysis techniques.

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

Complexity Explorer

Dynamical Systems and Chaos

Explore mathematical chaos theory, from basic functions to strange attractors, covering bifurcations, the butterfly effect, and pattern formation in complex systems.

• YouTube
• 17 hours 40 minutes
• On-Demand
• Free Video