Explore the evolution and applications of Lyapunov exponents in this comprehensive lecture by renowned mathematician Marcelo Viana. Delve into the ergodic theory of Lyapunov exponents, tracing its development from the 1960s to the present day. Gain insights into classical results and recent advancements in smooth dynamics, including topics such as non-uniform hyperbolicity, stable manifold theorem, and partially hyperbolic dynamics. Learn about the work of influential mathematicians like Furstenberg, Kesten, Oseledets, and Pesin, and discover how Lyapunov exponents have found crucial applications in various fields of mathematics. The lecture also covers related concepts like symplectic diffeomorphisms and direct perturbation of Lyapunov exponents, providing a thorough overview of this dynamic area of study.
Lyapunov Exponents, From the 1960's to the 2020's by Marcelo Viana
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
DATE: 24 September 2019, 16:00 to
ICTS-TIFR: An Overview
ICTS and its Mandate
The ICTS Campus - Imagined 2012
The ICTS Campus - Realised 2017
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ICTS Outreach
Thank You See You Again at ICTS
ICTP Mission
Research at ICTP
Pre-PhD Postgraduate Diploma at ICTP
Post-Diploma - Dynamical Systems students
ICTP Opportunities
Lyapunov exponents, from the 1960's to the 2020's
A few recent books
Research groups
Computational math labs
Graduate studies
Brazilian Mathematical Olympiad
Publications - education - popularization
National Math Festival 2020
New campus
Lyapunov stability
Extremal Lyapunov exponents
Lyapunov exponents
Non-uniform hyperbolicity
Stable manifold theorem
Partially hyperbolic dynamics
Smooth cocycles
Fibered Lyapunov exponents
Invariance principle
Lyapunov exponents of partially hyperbolic maps
Symplectic diffeomorphisms
Direct perturbation of Lyapunov exponents
Q&A
Taught by
International Centre for Theoretical Sciences
