Displaying similar documents to “An Upper Estimation for Topological Entropy of Diffeomorphisms.”

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...

The topological entropy versus level sets for interval maps

Jozef Bobok (2002)

Studia Mathematica

Similarity:

We answer affirmatively Coven's question [PC]: Suppose f: I → I is a continuous function of the interval such that every point has at least two preimages. Is it true that the topological entropy of f is greater than or equal to log 2?

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...

Uniform entropy vs topological entropy

Dikran Dikranjan, Hans-Peter A. Kunzi (2015)

Topological Algebra and its Applications

Similarity:

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.

Maximal entropy measures in dimension zero

Dawid Huczek (2012)

Colloquium Mathematicae

Similarity:

We prove that an invertible zero-dimensional dynamical system has an invariant measure of maximal entropy if and only if it is an extension of an asymptotically h-expansive system of equal topological entropy.

A remark on the topological entropies of covers and partitions

Pierre-Paul Romagnoli (2007)

Studia Mathematica

Similarity:

We study if the combinatorial entropy of a finite cover can be computed using finite partitions finer than the cover. This relates to an unsolved question in [R] for open covers. We explicitly compute the topological entropy of a fixed clopen cover showing that it is smaller than the infimum of the topological entropy of all finer clopen partitions.

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.