Continuity properties of Lyapunov exponents for surface diffeomorphisms

DOI10.1007/s00222-022-01132-xOpenAlexW3135829378MaRDI QIDQ2084781

Sylvain Crovisier, Jérôme Buzzi, Omri M. Sarig

Publication date: 13 October 2022

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.02400

zbMATH Keywords

invariant measuresLyapunov exponentsHausdorff dimensionSRB measures

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Partially hyperbolic systems and dominated splittings (37D30)

Related Items

Maximal measure and entropic continuity of Lyapunov exponents for \({\mathcal{C}}^r\) surface diffeomorphisms with large entropy, SRB measures for \(C^{\infty}\) surface diffeomorphisms

Cites Work

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• Random matrix products and measures on projective spaces
• Entropy structure
• Escape of mass and entropy for diagonal flows in real rank one situations
• Extremal Lyapunov exponents: an invariance principle and applications
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Volume growth and entropy
• Analycity properties of the characteristic exponents of random matrix products
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Ergodic theory on compact spaces
• Dimension and product structure of hyperbolic measures
• Intrinsic ergodicity of smooth interval maps
• Measures of maximal dimension for hyperbolic diffeomorphisms
• Entropy in the cusp and phase transitions for geodesic flows
• Symbolic extensions and smooth dynamical systems
• Continuity of Lyapunov exponents for cocycles with invariant holonomies
• The entropy theory of symbolic extensions
• Upper semi-continuity of entropy in non-compact settings
• Escape of entropy for countable Markov shifts
• The metric entropy of diffeomorphisms. II: Relations between entropy, exponents and dimension
• Effectivity of uniqueness of the maximal entropy measure on -adic homogeneous spaces
• Symbolic extensions in intermediate smoothness on surfaces
• surface diffeomorphisms with no maximal entropy measure
• Amount of failure of upper-semicontinuity of entropy in non-compact rank-one situations, and Hausdorff dimension
• Dimension estimates in smooth dynamics: a survey of recent results
• A proof of the estimation from below in Pesin's entropy formula
• Continuity of Lyapunov exponents for polynomial automorphisms of $\mathbb{C}^2$
• Dimension, entropy and Lyapunov exponents
• An inequality for the entropy of differentiable maps
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• A Relativised Variational Principle for Continuous Transformations
• Usc/fibred entropy structure and applications
• Escape of mass and entropy for geodesic flows
• Genericity of zero Lyapunov exponents
• (Dis)continuity of Lyapunov exponents
• Effective equidistribution of periodic orbits for subshifts of finite type
• Continuity of Lyapunov exponents for random two-dimensional matrices
• Lectures on Lyapunov Exponents
• Noncommuting Random Products
• Entropy for Group Endomorphisms and Homogeneous Spaces
• Entropies and volume growth of unstable manifolds