### Renormalized entropy solutions of scalar conservation laws

Philippe Bénilan, Jose Carrillo, Petra Wittbold (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Philippe Bénilan, Jose Carrillo, Petra Wittbold (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Gselmann, Eszter (2008)

Banach Journal of Mathematical Analysis [electronic only]

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

International Journal of Mathematics and Mathematical Sciences

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

International Journal of Mathematics and Mathematical Sciences

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Inder Jeet Taneja (1977)

Annales Polonici Mathematici

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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.

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.

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...

Brunon Kamiński, José de Sam Lazaro (2000)

Colloquium Mathematicae

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We investigate the properties of the entropy and conditional entropy of measurable partitions of unity in the space of essentially bounded functions defined on a Lebesgue probability space.

François Blanchard (1993)

Bulletin de la Société Mathématique de France

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Collet, P. (1998)

Documenta Mathematica

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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...

D. Vivona, M. Divari (2007)

Mathware and Soft Computing

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