Entropy for endomorphisms of LCA groups

DOI10.1016/J.TOPOL.2011.02.017zbMath1243.22007OpenAlexW2091561875MaRDI QIDQ429354

Simone Virili

Publication date: 19 June 2012

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2011.02.017

zbMATH Keywords

Haar measurelocally compact abelian groupsalgebraic entropycontinuous endomorphisms

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) Entropy and other invariants (28D20) Entropy in general topology (54C70)

Related Items (28)

Entropy on abelian groups ⋮ Topological entropy for locally linearly compact vector spaces ⋮ Dimension and entropy in compact topological groups ⋮ The addition theorem for locally monotileable monoid actions ⋮ Weakly weighted generalised quasi-metric spaces and semilattices ⋮ Entropy in a category ⋮ Additivity of the algebraic entropy for locally finite groups with permutable finite subgroups ⋮ Ore localization of amenable monoid actions and applications toward entropy -- addition formulas and the bridge theorem ⋮ Endomorphisms of abelian groups with small algebraic entropy ⋮ The connection between topological and algebraic entropy ⋮ Unnamed Item ⋮ The Bridge Theorem for totally disconnected LCA groups ⋮ FINITENESS OF TOPOLOGICAL ENTROPY FOR LOCALLY COMPACT ABELIAN GROUPS ⋮ Algebraic Yuzvinski formula ⋮ Algebraic Entropies for Abelian Groups with Applications to the Structure of Their Endomorphism Rings: A Survey ⋮ Algebraic Entropy in Locally Linearly Compact Vector Spaces ⋮ On a notion of entropy in coarse geometry ⋮ Algebraic entropy of endomorphisms of \(M\)-sets ⋮ Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space ⋮ Intrinsic algebraic entropy ⋮ Inertial properties in groups ⋮ Algebraic entropy on topologically quasihamiltonian groups ⋮ A property of the lamplighter group ⋮ A bridge theorem for the entropy of semigroup actions ⋮ Algebraic entropy on strongly compactly covered groups ⋮ Entropy on normed semigroups (towards a unifying approach to entropy) ⋮ Algebraic and Shannon entropies of commutative hypergroups and their connection with information and permutation entropies and with calculation of entropy for chemical algebras ⋮ Intrinsic entropy for generalized quasimetric semilattices

Cites Work

• Unnamed Item
• Entropy on abelian groups
• New and old facts about entropy in uniform spaces and topological groups
• Algebraic Yuzvinski formula
• Entropy on discrete Abelian groups
• Entropy of automorphisms on l.c.a. groups
• Algebraic entropy for Abelian groups
• Automorphisms of solenoids and p-adic entropy
• Algebraic and other entropies of group endomorphisms
• Topological Entropy
• Asymptotic Behavior of Products C p = C + ⋯+ C in Locally Compact Abelian Groups

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