Extremal Lyapunov exponents: an invariance principle and applications
type: Item
instance of: scholarly article
title: Extremal Lyapunov exponents: an invariance principle and applications
zbMATH Open document ID: 1196.37054
author: Artur Avila
author: Marcelo Viana
published in: Inventiones Mathematicae
publication date: 2010-06-21T00:00:00Z
review text: Dynamical systems with both hyperbolic and center behavior are studied. The authors present a new approach based on invariance principle and it is in terms of smooth cocycles. They use the extremal Lyapunov exponents to find the smallest and largest exponential rates of growth of the derivative along the fibers. Several other applications of this new approach are given as well.
reviewed by: Angela Slavova
Mathematics Subject Classification ID: 37D10
Mathematics Subject Classification ID: 37D25
zbMATH DE Number: 5723603
zbMATH Keywords: Lyapunov exponents
zbMATH Keywords: invariance principle
zbMATH Keywords: smooth cocycles
zbMATH Keywords: hyperbolic dynamical systems
MaRDI profile type: Publication
full work available at URL: s00222-010-0243-1
OpenAlex ID: W2013723323
cites work: SRB measures for partially hyperbolic systems whose central direction is mostly expanding
cites work: Q5401576
cites work: Simplicity of Lyapunov spectra: a sufficient criterion
cites work: Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture
cites work: Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows
cites work: Dimension and product structure of hyperbolic measures
cites work: Lyapunov exponents and relative entropy for a stochastic flow of diffeomorphisms
cites work: Genericity of zero Lyapunov exponents
cites work: C1-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents
cites work: The Lyapunov exponents of generic volume-preserving and symplectic maps
cites work: Continuity of Lyapunov exponents for random two-dimensional matrices
cites work: Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices. (Genericity of non-zero Lyapunov exponents for deterministic products of matrices)
cites work: SRB measures for partially hyperbolic systems whose central direction is mostly contracting
cites work: Lyapunov exponents with multiplicity 1 for deterministic products of matrices
cites work: A horseshoe with positive measure
cites work: On the ergodicity of partially hyperbolic systems
cites work: Furstenberg's theorem for nonlinear stochastic systems
cites work: Conformally natural extension of homeomorphisms of the circle
cites work: Q4002564
cites work: Realizing Rotation Vectors for Torus Homeomorphisms
cites work: Noncommuting Random Products
cites work: Stable ergodicity of certain linear automorphisms of the torus
cites work: Invariant manifolds
cites work: A regularity lemma for functions of several variables
cites work: Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
cites work: Ergodic automorphisms of \(T^ n\) are Bernoulli shifts
cites work: Q5573847
cites work: Propriétés ergodiques des mesures de Sinaï
cites work: The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
cites work: On the Bernoulli nature of systems with some hyperbolic structure
cites work: Q5646734
cites work: FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS
cites work: CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
cites work: Stably ergodic dynamical systems and partial hyperbolicity
cites work: An inequality for the entropy of differentiable maps
cites work: Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
cites work: Physical measures and absolute continuity for one-dimensional center direction
cites work: Statistical properties of dynamical systems with some hyperbolicity
cites work: Recurrence times and rates of mixing
DOI: 10.1007/S00222-010-0243-1
Recommended article: Q3706212
Recommended article: Q3979045
Recommended article: Q3734804
Recommended article: The problem of the inverse Lyapunov exponent and its applications
Recommended article: Q4839126
Recommended article: Estimates for principal Lyapunov exponents: a survey
Recommended article: Q5520197
Recommended article: Lyapunov Exponents and Uniform Weak Normally Repelling Invariant Sets
Recommended article: Bounds on the Ljapunov Exponent
Recommended article: Lyapunov Exponents
description: scientific article; zbMATH DE number 5723603