Algebraic entropies, Hopficity and co-Hopficity of direct sums of Abelian Groups

Brendan Goldsmith; Ketao Gong

The search session has expired. Please query the service again.

Displaying similar documents to “Algebraic entropies, Hopficity and co-Hopficity of direct sums of Abelian Groups”

Abelian groups of zero adjoint entropy

L. Salce, P. Zanardo (2010)

Colloquium Mathematicae

Similarity:

The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of...

The entropy of algebraic actions of countable torsion-free abelian groups

Richard Miles (2008)

Fundamenta Mathematicae

Similarity:

This paper is concerned with the entropy of an action of a countable torsion-free abelian group G by continuous automorphisms of a compact abelian group X. A formula is obtained that expresses the entropy in terms of the Mahler measure of a greatest common divisor, complementing earlier work by Einsiedler, Lind, Schmidt and Ward. This leads to a uniform method for calculating entropy whenever G is free. In cases where these methods do not apply, a possible entropy formula is conjectured....

On the modified entropy equation.

Gselmann, Eszter (2008)

Banach Journal of Mathematical Analysis [electronic only]

Similarity:

Quantum dynamical entropy revisited

Thomas Hudetz (1998)

Banach Center Publications

Similarity:

We define a new quantum dynamical entropy for a C*-algebra automorphism with an invariant state (and for an appropriate 'approximating' subalgebra), which entropy is a 'hybrid' of the two alternative definitions by Connes, Narnhofer and Thirring resp. by Alicki and Fannes (and earlier, Lindblad). We report on this entropy's properties and on three examples.

Renormalized entropy solutions of scalar conservation laws

Philippe Bénilan, Jose Carrillo, Petra Wittbold (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Entropy pairs of ℤ² and their directional properties

Kyewon Koh Park, Uijung Lee (2004)

Studia Mathematica

Similarity:

Topological and metric entropy pairs of ℤ²-actions are defined and their properties are investigated, analogously to ℤ-actions. In particular, mixing properties are studied in connection with entropy pairs.

Boltzmann-Gibbs entropy: Axiomatic characterization and application.

Chakrabarti, C.G., De, Kajal (2000)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Maličky-Riečan's entropy as a version of operator entropy

Bartosz Frej (2006)

Fundamenta Mathematicae

Similarity:

The paper deals with the notion of entropy for doubly stochastic operators. It is shown that the entropy defined by Maličky and Riečan in [MR] is equal to the operator entropy proposed in [DF]. Moreover, some continuity properties of the [MR] entropy are established.

On the branching property of entropy

Inder Jeet Taneja (1977)

Annales Polonici Mathematici

Similarity:

Shannon entropy: axiomatic characterization and application.

Chakrabarti, C.G., Chakrabarty, Indranil (2005)

International Journal of Mathematics and Mathematical Sciences

Similarity:

On the origin and development of some notions of entropy

Francisco Balibrea (2015)

Topological Algebra and its Applications

Similarity:

Discrete dynamical systems are given by the pair (X, f ) where X is a compact metric space and f : X → X a continuous maps. During years, a long list of results have appeared to precise and understand what is the complexity of the systems. Among them, one of the most popular is that of topological entropy. In modern applications other conditions on X and f have been considered. For example X can be non-compact or f can be discontinuous (only in a finite number of points and with bounded...

Entropy dimension and variational principle

Young-Ho Ahn, Dou Dou, Kyewon Koh Park (2010)

Studia Mathematica

Similarity:

Recently the notions of entropy dimension for topological and measurable dynamical systems were introduced in order to study the complexity of zero entropy systems. We exhibit a class of strictly ergodic models whose topological entropy dimensions range from zero to one and whose measure-theoretic entropy dimensions are identically zero. Hence entropy dimension does not obey the variational principle.

A new approach to mutual information

Fumio Hiai, Dénes Petz (2007)

Banach Center Publications

Similarity:

A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.

A disjointness theorem involving topological entropy

François Blanchard (1993)

Bulletin de la Société Mathématique de France

Similarity:

Fiber entropy and conditional variational principles in compact non-metrizable spaces

Tomasz Downarowicz, Jacek Serafin (2002)

Fundamenta Mathematicae

Similarity:

We consider a pair of topological dynamical systems on compact Hausdorff (not necessarily metrizable) spaces, one being a factor of the other. Measure-theoretic and topological notions of fiber entropy and conditional entropy are defined and studied. Abramov and Rokhlin's definition of fiber entropy is extended, using disintegration. We prove three variational principles of conditional nature, partly generalizing some results known before in metric spaces: (1) the topological conditional...