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… (More)

We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem… (More)

We introduce the mathematical concept of multifractality and describe various multifractal spectra for dynamical systems, including spectra for dimensions and spectra for entropies. We support the… (More)

Designed to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account of modern smooth ergodic theory. Among… (More)

We prove that every hyperbolic measure invariant under a C diffeomorphism of a smooth Riemannian manifold possesses asymptotically “almost” local product structure, i.e., its density can be… (More)

In this paper we establish the complete multifractal formalism for equilibrium measures for Hölder continuous conformal expanding maps and expanding Markov Moran-like geometric constructions.… (More)

We consider coupled map lattices of hyperbolic type, i.e., chains of weakly interacting hyperbolic sets (attractors) over multi-dimensional lattices. We describe the thermodynamic formalism of the… (More)

Introduction 1 1. Lyapunov exponents of dynamical systems 3 2. Examples of systems with nonzero exponents 6 3. Lyapunov exponents associated with sequences of matrices 18 4. Cocycles and Lyapunov… (More)

We establish the complete multifractal formalism for Gibbs measures for confor-mal expanding maps and Markov Moran geometric constructions. Examples include Markov maps of an interval, hyperbolic… (More)