Topological pressure of historic set for \(\mathbb{Z}^d\)-actions

DOI10.1016/j.jmaa.2011.11.066zbMath1238.37003OpenAlexW1969895357MaRDI QIDQ663712

Xiaoyao Zhou, Ercai Chen

Publication date: 27 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.11.066

zbMATH Keywords

multifractalstopological pressurehistoric set\(\mathbb Z^d\)-actions

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (5)

THE PRESSURE OF THE HISTORIC SET FOR ERGODIC AUTOMORPHISMS OF ABELIAN GROUPS ⋮ On the topological entropy of the irregular part of v-statistics multifractal spectra ⋮ Brin-Katok formula for the measure theoretic \(r\)-entropy ⋮ Unnamed Item ⋮ Quantitative recurrence properties in the historic set for symbolic systems

Cites Work

• Unnamed Item
• The irregular set for maps with the specification property has full topological pressure
• TOPOLOGICAL PRESSURE OF THE SET OF GENERIC POINTS FOR Zd-ACTIONS
• A variational principle for topological pressure for certain non-compact sets
• Statistical Mechanics on a Compact Set with Z p Action Satisfying Expansiveness and Specification
• On the variational principle for the topological entropy of certain non-compact sets
• On the topological entropy of saturated sets
• Orbits with historic behaviour, or non-existence of averages
• Topological entropy for divergence points

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