A minimum principle for Lyapunov exponents and a higher-dimensional version of a theorem of Mañé

DOI10.1007/BF02972681zbMath1122.37024arXivmath/0309057MaRDI QIDQ2457728

Isabel Rios, Stefano Luzzatto, Yong-Luo Cao

Publication date: 23 October 2007

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0309057

zbMATH Keywords

invariant measuresnonuniform hyperbolicityuniform hyperbolicityhyperbolic repelling

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (6)

Thermodynamical and spectral phase transition for local diffeomorphisms in the circle ⋮ Pointwise hyperbolicity implies uniform hyperbolicity ⋮ Uniform hyperbolicity for random maps with positive Lyapunov exponents ⋮ Topological invariance of the sign of the Lyapunov exponents in one-dimensional maps ⋮ Thermodynamic formalism for a family of non-uniformly hyperbolic horseshoes and the unstable Jacobian ⋮ Equilibrium Measures at Temperature Zero for Hénon-Like Maps at the First Bifurcation

Cites Work

• Hyperbolicity, sinks and measure in one dimensional dynamics
• Non-uniform hyperbolicity and universal bounds for \(S\)-unimodal maps
• Characteristic exponents and invariant manifolds in Hilbert space
• Ergodic Properties of Linear Dynamical Systems
• Continuous subadditive processes and formulae for Lyapunov characteristic exponents
• Non-zero Lyapunov exponents and uniform hyperbolicity
• On the uniform hyperbolicity of some nonuniformly hyperbolic systems
• Semi-uniform ergodic theorems and applications to forced systems
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