Displaying similar documents to “A note on the uniqueness of entropy solutions to first order quasilinear equations.”

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

Bartosz Frej (2006)

Fundamenta Mathematicae


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.

Entropy pairs of ℤ² and their directional properties

Kyewon Koh Park, Uijung Lee (2004)

Studia Mathematica


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.

On the origin and development of some notions of entropy

Francisco Balibrea (2015)

Topological Algebra and its Applications


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...

A note on the entropy of a doubly stochastic operator

Brunon Kamiński, José de Sam Lazaro (2000)

Colloquium Mathematicae


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.

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

Tomasz Downarowicz, Jacek Serafin (2002)

Fundamenta Mathematicae


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...