On the modified entropy equation.
Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Chakrabarti, C.G., Chakrabarty, Indranil (2005)
International Journal of Mathematics and Mathematical Sciences
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Bartosz Frej (2006)
Fundamenta Mathematicae
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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.
Young-Ho Ahn, Dou Dou, Kyewon Koh Park (2010)
Studia Mathematica
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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.
Philippe Bénilan, Jose Carrillo, Petra Wittbold (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Chakrabarti, C.G., De, Kajal (2000)
International Journal of Mathematics and Mathematical Sciences
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Inder Jeet Taneja (1977)
Annales Polonici Mathematici
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Gang Liao, Marcelo Viana, Jiagang Yang (2013)
Journal of the European Mathematical Society
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We prove that every diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub’s entropy conjecture: the entropy is bounded from below by the spectral radius in homology. Moreover, they admit principal symbolic extensions, and the topological entropy and metrical entropy vary continuously with the map. In contrast, generic diffeomorphisms with persistent tangencies are not entropy expansive. ...
Christian Mauduit, Carlos Gustavo Moreira (2010)
Acta Arithmetica
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Kyewon Koh Park, Uijung Lee (2004)
Studia Mathematica
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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.
Tomasz Downarowicz, Jacek Serafin (2002)
Fundamenta Mathematicae
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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...
Francisco Balibrea (2015)
Topological Algebra and its Applications
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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...
Dikran Dikranjan, Hans-Peter A. Kunzi (2015)
Topological Algebra and its Applications
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We discuss the connection between the topological entropy and the uniform entropy and answer several open questions from [10, 15]. We also correct several erroneous statements given in [10, 18] without proof.
Fumio Hiai, Takuho Miyamoto (2010)
Banach Center Publications
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A new concept of mutual pressure is introduced for potential functions on both continuous and discrete compound spaces via discrete micro-states of permutations, and its relations with the usual pressure and the mutual information are established. This paper is a continuation of the paper of Hiai and Petz in Banach Center Publications, Vol. 78.
François Blanchard (1993)
Bulletin de la Société Mathématique de France
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