The metric entropy of endomorphisms

DOI10.1007/S00220-009-0859-4zbMath1196.37017OpenAlexW1967864064MaRDI QIDQ1048109

Lin Shu

Publication date: 11 January 2010

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

Full work available at URL: https://doi.org/10.1007/s00220-009-0859-4

zbMATH Keywords

entropyLyapunov exponentsfolding entropy

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35)

Related Items (13)

Entropy via preimage structure ⋮ Ergodic properties for some non-expanding non-reversible systems ⋮ Preimage pressure, stable pressure and equilibrium states ⋮ Forward expansiveness and entropies for subsystems of \(\mathbb{Z}_+^k\)-actions ⋮ SRB measures for partially hyperbolic attractors of local diffeomorphisms ⋮ Smooth ergodic theory of \(\mathbb{Z}^d \)-actions ⋮ Preimage entropy and stable entropy on subsets ⋮ Ruelle inequality of folding type for \(C^{1+\alpha}\) maps ⋮ 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 ⋮ On some coding and mixing properties for a class of chaotic systems ⋮ Dimension theory for invariant measures of endomorphisms ⋮ On preimage entropy, folding entropy and stable entropy

Cites Work

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• Entropy formula for endomorphisms: relations between entropy, exponents and dimension
• Dimension theory for invariant measures of endomorphisms
• Invariant measures satisfying an equality relating entropy, folding entropy and negative Lyapunov exponents
• 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
• Positivity of entropy production in nonequilibrium statistical mechanics
• Dimension and product structure of hyperbolic measures
• Ruelle inequality relating entropy, folding entropy and negative Lyapunov exponents
• Smooth ergodic theory of random dynamical systems
• SRB measures and Pesin’s entropy formula for endomorphisms
• A proof of Pesin's formula
• Ergodic theory for axiom A endomorphisms
• Ergodic theory of chaos and strange attractors

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