Entropy on abelian groups

DOI10.1016/j.aim.2016.04.020zbMath1368.37015OpenAlexW1559128742WikidataQ105773370 ScholiaQ105773370MaRDI QIDQ291785

Anna Giordano Bruno, Dikran Dikranjan

Publication date: 10 June 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2016.04.020

zbMATH Keywords

Mahler measureabelian groupdiscrete dynamical systemaddition theoremalgebraic entropygroup endomorphismLehmer problem

Mathematics Subject Classification ID

Related Items (44)

Some properties of the growth and of the algebraic entropy of group endomorphisms ⋮ Topological entropy for locally linearly compact vector spaces ⋮ Dimension and entropy in compact topological groups ⋮ The addition theorem for locally monotileable monoid actions ⋮ The entropy of semi-independent hyper MV-algebra dynamical systems ⋮ Two new proofs concerning the intrinsic algebraic entropy ⋮ Algebraic entropy for amenable semigroup actions ⋮ A soft introduction to algebraic entropy ⋮ When the intrinsic algebraic entropy is not really intrinsic ⋮ Weakly weighted generalised quasi-metric spaces and semilattices ⋮ New and old facts about entropy in uniform spaces and topological groups ⋮ Entropy in a category ⋮ The addition theorem for two-step nilpotent torsion groups ⋮ 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 ⋮ Adjoint entropy vs topological entropy ⋮ Entropy for endomorphisms of LCA groups ⋮ Endomorphisms of abelian groups with small algebraic entropy ⋮ Unnamed Item ⋮ The Bridge Theorem for totally disconnected LCA groups ⋮ The Pinsker subgroup of an algebraic flow ⋮ 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 ⋮ Corner’s Realization Theorems from the Viewpoint of Algebraic Entropy ⋮ Topological and metric entropy for group and semigroup actions ⋮ On a notion of entropy in coarse geometry ⋮ Algebraic entropy of endomorphisms of \(M\)-sets ⋮ Intrinsic algebraic entropy ⋮ Inertial properties in groups ⋮ Milnor-Wolf theorem for group endomorphisms ⋮ Metric versus topological receptive entropy of semigroup actions ⋮ Algebraic entropies of commuting endomorphisms of torsion abelian groups ⋮ Algebraic entropy on topologically quasihamiltonian groups ⋮ Some applications of algebraic entropy to the proof of Milnor-Wolf theorem ⋮ On uniformly fully inert subgroups of abelian groups ⋮ 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) ⋮ Intrinsic valuation entropy ⋮ Generalized quasi-metric semilattices ⋮ 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

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• New and old facts about entropy in uniform spaces and topological groups
• Entropy for endomorphisms of LCA groups
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• Algebraic Yuzvinski formula
• The Pinsker subgroup of an algebraic flow
• Adjoint algebraic entropy.
• Entropy on discrete Abelian groups
• Entropy of automorphisms on l.c.a. groups
• Finite rank torsion free Abelian groups and rings
• Heights of polynomials and entropy in algebraic dynamics
• Factorization of certain cyclotomic functions
• Entropy in a category
• Intrinsic algebraic entropy
• Endomorphisms of abelian groups with small algebraic entropy
• The Bridge Theorem for totally disconnected LCA groups
• Discrete dynamical systems in group theory
• Growth rate of an endomorphism of a group
• Algebraic Entropy of Shift Endomorphisms on Abelian Groups
• Algebraic entropy for Abelian groups
• Automorphisms of solenoids and p-adic entropy
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• A GENERALIZATION OF THE CONCEPT OF LENGTH
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• Topological Entropy and Algebraic Entropy for group endomorphisms
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• ALGEBRAIC ENTROPY OF ENDOMORPHISMS OVER LOCAL ONE-DIMENSIONAL DOMAINS

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