The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
From MaRDI portal
Publication:1083739
DOI10.2307/1971328zbMath0605.58028OpenAlexW2162696617MaRDI QIDQ1083739
Lai-Sang Young, François Ledrappier
Publication date: 1985
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/1971328
Lyapunov exponentsdimensionmetric entropyPesin's entropy formulaunstable manifoldssmooth ergodic theory
Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20)
Related Items (only showing first 100 items - show all)
GEOMETRICAL AND MEASURE-THEORETIC STRUCTURES OF MAPS WITH A MOSTLY EXPANDING CENTER ⋮ Measure rigidity for random dynamics on surfaces and related skew products ⋮ Packing Entropy of Saturated Sets for Nonuniformly Hyperbolic Systems ⋮ Unnamed Item ⋮ Smoothness of stable holonomies inside center-stable manifolds ⋮ Efficient Computation of Linear Response of Chaotic Attractors with One-Dimensional Unstable Manifolds ⋮ The information topology and true laminations for diffeomorphisms ⋮ C1 actions on manifolds by lattices in Lie groups ⋮ Robust minimality of strong foliations for DA diffeomorphisms: 𝑐𝑢-volume expansion and new examples ⋮ Understanding Chaotic Dynamical Systems ⋮ Rigorous justification for the space–split sensitivity algorithm to compute linear response in Anosov systems ⋮ Invariant family of leaf measures and the Ledrappier–Young property for hyperbolic equilibrium states ⋮ Thermodynamical u-formalism I: measures of maximal u-entropy for maps that factor over Anosov ⋮ Disintegrations of non‐hyperbolic ergodic measures along the center foliation of DA maps ⋮ Hyperbolic Lyapunov–Perron regular points and smooth invariant measures ⋮ Variation of measures of maximal \(u\)-entropy ⋮ Hyperbolicity of maximal entropy measures for certain maps isotopic to Anosov diffeomorphisms ⋮ Rigidity, lattices, and invariant measures beyond homogeneous dynamics ⋮ Maximal measure and entropic continuity of Lyapunov exponents for \({\mathcal{C}}^r\) surface diffeomorphisms with large entropy ⋮ Learning Theory for Dynamical Systems ⋮ Self‐adjoint Laplacians and symmetric diffusions on hyperbolic attractors ⋮ Random dynamics on real and complex projective surfaces ⋮ SRB measures for partially hyperbolic attractors of local diffeomorphisms ⋮ Open sets of partially hyperbolic skew products having a unique SRB measure ⋮ On the Ledrappier–Young formula for self-affine measures ⋮ Smooth ergodic theory of \(\mathbb{Z}^d \)-actions ⋮ Equilibrium states for certain partially hyperbolic attractors ⋮ An invitation to \(SL_2(\mathbb{R})\) cocycles over random dynamics ⋮ SRB measures for \(C^{\infty}\) surface diffeomorphisms ⋮ Unnamed Item ⋮ Comparing chaotic and random dynamical systems ⋮ Optimal Brownian Stopping When the Source and Target Are Radially Symmetric Distributions ⋮ Unstable entropy of partially hyperbolic diffeomorphisms along non-compact subsets ⋮ Hyperbolic graphs: Critical regularity and box dimension ⋮ The ergodic theory of discrete isometry groups on manifolds of variable negative curvature ⋮ CENTRAL LIMIT THEOREM FOR DIMENSION OF GIBBS MEASURES IN HYPERBOLIC DYNAMICS ⋮ Invariant measures for higher-rank hyperbolic abelian actions ⋮ Unstable entropy and unstable pressure for random partially hyperbolic dynamical systems ⋮ Class degree and relative maximal entropy ⋮ Phase transitions for the geodesic flow of a rank one surface with nonpositive curvature ⋮ A new entropy formula of Ledrappier–Young type for linear toral dynamics ⋮ The metric entropy of random dynamical systems in a Banach space: Ruelle inequality ⋮ \(p\)-adic foliation and equidistribution ⋮ Noise Induced Order: Stochastic Resonance ⋮ Entropy Analysis of Noise Contaminated Sequences ⋮ Local product structure for Equilibrium States ⋮ Conditions for the Existence of SBR Measures for “Almost Anosov” Diffeomorphisms ⋮ A new criterion of physical measures for partially hyperbolic diffeomorphisms ⋮ On preimage entropy, folding entropy and stable entropy ⋮ On the historical behavior of singular hyperbolic attractors ⋮ Dimension of hyperbolic measures of random diffeomorphisms ⋮ Simplicity of Lyapunov spectrum for linear cocycles over non-uniformly hyperbolic systems ⋮ -openness of non-uniform hyperbolic diffeomorphisms with bounded -norm ⋮ Statistical stability of saddle-node arcs ⋮ Strange Attractors for Periodically Forced Parabolic Equations ⋮ Equilibrium states for Mañé diffeomorphisms ⋮ Triangular Gatzouras–Lalley-type planar carpets with overlaps ⋮ Unique equilibrium states, large deviations and Lyapunov spectra for the Katok map ⋮ Exact dimensionality and Ledrappier-Young formula for the Furstenberg measure ⋮ Ergodic properties of Brownian motion on covers of compact negatively-curve manifolds ⋮ The work of Einsiedler, Katok and Lindenstrauss on the Littlewood conjecture ⋮ Unstable entropy in smooth ergodic theory * ⋮ Statistical properties of physical-like measures* ⋮ Fractal Geometry of Bedford-McMullen Carpets ⋮ Entropies and volume growth of unstable manifolds ⋮ The Pesin entropy formula for diffeomorphisms with dominated splitting ⋮ Entropy inequalities for semigroup actions ⋮ Unstable entropies and dimension theory of partially hyperbolic systems ⋮ Existence of physical measures in some excitation–inhibition networks* ⋮ Rigidity properties for commuting automorphisms on tori and solenoids ⋮ SRB measures in chaotic dynamical systems ⋮ Entropy formula for systems with inducing schemes ⋮ Lower bound in Pesin formula of C 1 interval maps* ⋮ Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows ⋮ Notes on the multiplicative ergodic theorem ⋮ Non-uniformly hyperbolic billiards ⋮ Stably ergodic diffeomorphisms which are not partially hyperbolic ⋮ SRB measures and homoclinic relation for endomorphisms ⋮ Exponential mixing and smooth classification of commuting expanding maps ⋮ Normal forms for non-uniform contractions ⋮ A Grobman-Hartman theorem for general nonuniform exponential dichotomies ⋮ Invariant two-forms for geodesic flows ⋮ Entropy formula for random transformations ⋮ Ergodic hyperbolic attractors of endomorphisms ⋮ When a physical-like measure is physical or SRB? ⋮ A dimension formula for Bernoulli convolutions ⋮ Dimension spectrum of Axiom A diffeomorphisms. II: Gibbs measures ⋮ Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space ⋮ Locating resonances for axiom A dynamical systems ⋮ Noncommutative algebras for hyperbolic diffeomorphisms ⋮ Intrinsic ergodicity of affine maps in \([0,1^ d\)] ⋮ On the hybrid control of metric entropy for dominated splittings ⋮ Formula of entropy along unstable foliations for \(C^1\) diffeomorphisms with dominated splitting ⋮ Ruelle's inequality in negative curvature ⋮ Multi-invariant measures and subsets on nilmanifolds ⋮ Dimension formula for random transformations ⋮ Dimensions of invariant sets of expanding maps ⋮ Unstable entropies and variational principle for partially hyperbolic diffeomorphisms ⋮ Fluctuations of Lyapunov vectors in large volume limit and the information-flow configuration in space-time dynamics ⋮ Deformation rate of boundaries in Anosov and related systems
This page was built for publication: The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
