Dimension theory for invariant measures of endomorphisms

DOI10.1007/S00220-010-1059-YzbMath1217.37021OpenAlexW2042727187MaRDI QIDQ985707

Lin Shu

Publication date: 6 August 2010

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-010-1059-y

zbMATH Keywords

invariant measureshyperbolic measuresLyapunov dimension of measurerandom endomorphismsRiemannian manifolds without boundary

Mathematics Subject Classification ID

Invariant manifold theory for dynamical systems (37D10) Dimension theory of smooth dynamical systems (37C45)

Related Items (5)

A dimension associated with a cutting of the square of a Gibbs measure ⋮ Dimension of invariant measures for affine iterated function systems ⋮ A dichotomy for the dimension of SRB measure ⋮ A new entropy formula of Ledrappier–Young type for linear toral dynamics ⋮ The metric entropy of endomorphisms

Cites Work

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• Smooth ergodic theory for endomorphisms
• Entropy formula for endomorphisms: relations between entropy, exponents and dimension
• Invariant measures satisfying an equality relating entropy, folding entropy and negative Lyapunov exponents
• The metric entropy of endomorphisms
• The Lyapunov dimension of strange attractors
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki
• Dimension formula for random transformations
• Positivity of entropy production in nonequilibrium statistical mechanics
• Entropy formula of Pesin type for noninvertible random dynamical systems
• Dimension and product structure of hyperbolic measures
• On the spectra of randomly perturbed expanding maps
• Ruelle inequality relating entropy, folding entropy and negative Lyapunov exponents
• A note on the relationship of pointwise dimension of an invariant measure and its natural extension
• SRB measures and Pesin’s entropy formula for endomorphisms
• Dimension, entropy and Lyapunov exponents
• Dimension of invariant measures for maps with exponent zero
• A proof of Pesin's formula
• Dimension and invertibility of hyperbolic endomorphisms with singularities
• A dimension formula for endomorphisms—the Belykh family
• Ergodic theory for axiom A endomorphisms
• Ergodic theory of chaos and strange attractors
• Dimension of hyperbolic measures of random diffeomorphisms

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