The Katok's entropy formula for amenable group actions

DOI10.3934/dcds.2018195zbMath1396.37009OpenAlexW2809616239MaRDI QIDQ1661180

Xiaojun Huang, Jinsong Liu, Chang Rong Zhu

Publication date: 16 August 2018

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2018195

zbMATH Keywords

topological entropyamenable groupShannon-McMillan-Breiman theorem

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Topological entropy (37B40) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (5)

An alternative definition of topological entropy for amenable group actions ⋮ Localized topological pressure for amenable group actions ⋮ Topological \(r\)-entropy and measure theoretic \(r\)-entropy for amenable group actions ⋮ A Billingsley-type theorem for the pressure of an action of an amenable group ⋮ A variational principle of topological pressure on subsets for amenable group actions

Cites Work

• Local entropy theory for a countable discrete amenable group action
• Topological pressure for sub-additive potentials of amenable group actions
• Entropy of automorphisms arising from dynamical systems through discrete groups with amen\-able actions
• Return times, recurrence densities and entropy for actions of some discrete amenable groups
• Entropy and isomorphism theorems for actions of amenable groups
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Entropy and mixing for amenable group actions
• Pointwise theorems for amenable groups.
• The spectrum of completely positive entropy actions of countable amenable groups
• Almost-additive ergodic theorems for amenable groups
• Pointwise ergodic theorems beyond amenable groups
• Topological Entropy
• Fuglede–Kadison determinants and entropy for actions of discrete amenable groups
• Entropy for Group Endomorphisms and Homogeneous Spaces
• ON THE RELATIONS AMONG VARIOUS ENTROPY CHARACTERISTICS OF DYNAMICAL SYSTEMS
• Ergodic Theory

This page was built for publication: The Katok's entropy formula for amenable group actions