Uncountably many maximizing measures for a dense subset of continuous functions

DOI10.1088/1361-6544/aaaf47zbMath1394.37054arXiv1704.05616OpenAlexW2797205407MaRDI QIDQ4569302

Mao Shinoda

Publication date: 28 June 2018

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.05616

zbMATH Keywords

Choquet simplexergodic optimizationmaximizing measure

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Symbolic dynamics (37B10) Convex sets in topological linear spaces; Choquet theory (46A55)

Related Items

Arcwise connectedness of the set of ergodic measures of hereditary shifts, Typical ground states for large sets of interactions, 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, Lyapunov optimization for non-generic one-dimensional expanding Markov maps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ground states are generically a periodic orbit
• Ergodic theory and statistical mechanics
• Ergodic optimization for generic continuous functions
• Invariant measures of minimal post-critical sets of logistic maps
• On the zero-temperature limit of Gibbs states
• On the connectedness of ergodic systems
• Cohomology classes of dynamically non-negative \(C^ k\) functions.
• Entropy and maximizing measures of generic continuous functions
• Ergodic optimization
• La condition de Walters
• Lyapunov minimizing measures for expanding maps of the circle
• On density of ergodic measures and generic points
• Decomposition of dynamical systems on an interval
• On the uniqueness of the equilibrium state
• Specification on the interval
• Ergodic Optimization of Prevalent Super-continuous Functions
• Path connectedness and entropy density of the space of hyperbolic ergodic measures
• On Dynamical Systems With the Specification Property
• Thermodynamic Formalism
• Ergodic optimization of super-continuous functions on shift spaces
• Lectures on Choquet's theorem