On ergodic measures with negative Lyapunov exponents

Lyapunov Exponents and Smooth Ergodic Theory

This book provides a systematic introduction to smooth ergodic theory, including the general theory of Lyapunov exponents, nonuniform hyperbolic theory, stable manifold theory emphasizing absolute continuity of invariant foliations, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. The book can be used as a primary textbook for a special topics course on nonuniform hy...

Lectures on Lyapunov Exponents and Smooth Ergodic Theory

1. Lyapunov Exponents for Differential Equations 2. Abstract Theory of Lyapunov Exponents 3. Regularity of Lyapunov Exponents Associated with Differential Equations 4. Lyapunov Stability Theory 5. The Oseledets Decomposition 6. Dynamical Systems with Nonzero Lyapunov Exponents. Multiplicative Ergodic Theorem 7. Nonuniform Hyperbolicity. Regular Sets 8. Examples of Nonuniformly Hyperbolic System...

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

Estimating Invariant Measures and Lyapunov Exponents

This paper describes a method for obtaining rigorous numerical bounds on time averages for a class of one-dimensional expanding maps. The idea is to directly estimate the absolutely continuous invariant measure for these maps, without computing trajectories. The main theoretical result is a bound on the convergence rate of the Frobenius-Perron operator for such maps. The method is applied to es...

Lectures on Lyapunov exponents