Relative topological entropy for actions of non-discrete groups on compact spaces in the context of cut and project schemes

DOI10.1007/s10884-020-09838-3zbMath1467.37020arXiv1901.08985OpenAlexW3013277029MaRDI QIDQ2025680

Thomas Hauser

Publication date: 14 May 2021

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.08985

zbMATH Keywords

entropyuniform spaceamenable groupuniform latticeBowen formulaFølner sequencecut and project schemeOrnstein-Weiss lemmaVan Hove sequence

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Topological entropy (37B40) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Dynamics in general topological spaces (37B02)

Related Items (4)

Amorphic complexity of group actions with applications to quasicrystals ⋮ A note on entropy of Delone sets ⋮ Irregular model sets and tame dynamics ⋮ Leptin densities in amenable groups

Cites Work

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• Topological entropy, pseudo-orbits and uniform spaces
• Metric geometry of locally compact groups
• New and old facts about entropy in uniform spaces and topological groups
• Ergodic properties of visible lattice points
• Tail variational principle for a countable discrete amenable group action
• Spectral notions of aperiodic order
• A Banach space-valued ergodic theorem for amenable groups and applications
• Local entropy theory for a countable discrete amenable group action
• On pattern entropy of weak model sets
• Ergodic theory and statistical mechanics
• Entropy and isomorphism theorems for actions of amenable groups
• Quasicrystals and discrete geometry. Proceedings of the 1995 fall programme at The Fields Institute, Toronto, Canada
• The Abramov-Rokhlin entropy addition formula for amenable group actions
• \(p\)-adic numbers: An introduction.
• Approximate lattices
• Tilings of amenable groups
• Almost periodic measures and long-range order in Meyer sets
• Variational characterization of topological entropy of continuous transformation groups. Case of actions on \(\mathbb{R}{}^ n\)
• Mean topological dimension
• Topological invariants of dynamical systems and spaces of holomorphic maps. I.
• An analogue of Fekete's lemma for subadditive functions on cancellative amenable semigroups
• Conditional entropy and fiber entropy for amenable group actions
• Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies
• Bowen entropy for actions of amenable groups
• The variational principle
• Topological Entropy and Uniform Spaces
• Entropy theory without a past
• Directions in Mathematical Quasicrystals
• Aperiodic order and spherical diffraction, I: auto-correlation of regular model sets
• Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra
• Introduction to Dynamical Systems
• Model sets with positive entropy in Euclidean cut and project schemes
• Approximate Lattices and Meyer Sets in Nilpotent Lie Groups
• Operator Theoretic Aspects of Ergodic Theory
• Local entropy theory of a random dynamical system
• Topological Entropy Bounds Measure-Theoretic Entropy
• Entropy for Group Endomorphisms and Homogeneous Spaces
• Relating Topological Entropy and Measure Entropy
• Irregular model sets and tame dynamics
• Principles of harmonic analysis
• Lectures on amenability
• Entropy theory from the orbital point of view

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