Entropy and maximizing measures of generic continuous functions

DOI10.1016/j.crma.2008.01.006zbMath1131.37005OpenAlexW2024483475MaRDI QIDQ2472988

Julien Brémont

Publication date: 25 February 2008

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2008.01.006

zbMATH Keywords

variational probleminvariant measureszero entropyergodic optimization

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Topological entropy (37B40) Dynamical systems involving one-parameter continuous families of measure-preserving transformations (37A10)

Related Items (15)

Typical properties of ergodic optimization for asymptotically additive potentials ⋮ Ergodic optimization for some dynamical systems beyond uniform hyperbolicity ⋮ Uncountably many maximizing measures for a dense subset of continuous functions ⋮ Typical ground states for large sets of interactions ⋮ A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory ⋮ Constrained ergodic optimization for asymptotically additive potentials ⋮ Topological structures on saturated sets, optimal orbits and equilibrium states ⋮ Ergodic optimization restricted on certain subsets of invariant measures ⋮ A convex analysis approach to the metric mean dimension: limits of scaled pressures and variational principles ⋮ Ergodic optimization for hyperbolic flows and Lorenz attractors ⋮ Measures with maximum total exponent and generic properties of \(C^1\) expanding maps ⋮ Lyapunov optimization for non-generic one-dimensional expanding Markov maps ⋮ Dynamics on the graph of the torus parametrization ⋮ Sturmian maximizing measures for the piecewise-linear cosine family ⋮ Ergodic optimization in dynamical systems

Cites Work

• Ergodic theory on compact spaces
• Cohomology classes of dynamically non-negative \(C^ k\) functions.
• Ergodic optimization
• La condition de Walters
• Lyapunov optimizing measures for C1 expanding maps of the circle
• Livsic theorems, maximizing measures and the stable norm
• Thermodynamic Formalism
• Finite flowers and maximizing measures for generic Lipschitz functions on the circle

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