On the topological entropy of saturated sets for amenable group actions
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Publication:6142267
DOI10.1007/s10884-023-10302-1arXiv2008.05843OpenAlexW4387974884MaRDI QIDQ6142267
Xiankun Ren, Yun Hua Zhou, Xue Ting Tian
Publication date: 21 December 2023
Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.05843
Topological entropy (37B40) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)
Cites Work
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- Local entropy theory for a countable discrete amenable group action
- Non-uniform specification and large deviations for weak Gibbs measures
- Ergodic theory and statistical mechanics
- Different asymptotic behavior versus same dynamical complexity: recurrence \& (ir)regularity
- Almost additive multifractal analysis
- Dimension and recurrence in hyperbolic dynamics
- Multifractal formalism derived from thermodynamics for general dynamical systems
- Lyapunov spectrum of asymptotically sub-additive potentials
- The Shannon-McMillan-Breiman theorem for a class of amenable groups
- Topological pressure and the variational principle for noncompact sets
- Entropy and isomorphism theorems for actions of amenable groups
- A generalized Shannon-McMillan theorem for the action of an amenable group on a probability space
- Higher-dimensional multifractal analysis
- Pointwise theorems for amenable groups.
- Topological pressure of generic points for amenable group actions
- Periodic measures are dense in invariant measures for residually finite amenable group actions with specification
- Tilings of amenable groups
- A multifractal formalism
- Large deviations for \(\mathbb{Z}^ d\)-actions
- Multifractal spectra and multifractal rigidity for horseshoes
- Sets of ``non-typical points have full topological entropy and full Hausdorff dimension
- Generic points of invariant measures for an amenable residually finite group actions with the weak specification property
- Homoclinic groups, IE groups, and expansive algebraic actions
- Topological dimension and dynamical systems. Translated from the French by the author
- Topological entropy of level sets of empirical measures for non-uniformly expanding maps
- Bowen entropy for actions of amenable groups
- Variational principles and mixed multifractal spectra
- Irregular sets, the $đ˝$-transformation and the almost specification property
- Variational equalities of entropy in nonuniformly hyperbolic systems
- Multifractal analysis for weak Gibbs measures: from large deviations to irregular sets
- Multifractal analysis of weak Gibbs measures for non-uniformly expanding C1 maps
- On the irregular points for systems with the shadowing property
- Local Entropy, Metric Entropy and Topological Entropy for Countable Discrete Amenable Group Actions
- On minimal centers of attraction and generic points.
- On the variational principle for the topological entropy of certain non-compact sets
- NORMAL AND NON-NORMAL POINTS OF SELF-SIMILAR SETS AND DIVERGENCE POINTS OF SELF-SIMILAR MEASURES
- Quasi-uniform convergence in dynamical systems generated by an amenable group action
- Large deviations estimates for dynamical systems without the specification property. Application to the β-shifts
- On Dynamical Systems With the Specification Property
- Ergodic properties of invariant measures for C1+Îą non-uniformly hyperbolic systems
- The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples
- Topological Entropy for Noncompact Sets
- On the topological entropy of saturated sets
- The Lyapunov spectrum of some parabolic systems
- Transitively-saturated property, Banach recurrence and Lyapunov regularity
- On the Space of Invariant Measures for Hyperbolic Flows
- Ergodic Theory
- Multifractal analysis of hyperbolic flows
