Approximating entropy of maps of the interval
Louis Block, Ethan M. Coven (1989)
Banach Center Publications
Similarity:
Louis Block, Ethan M. Coven (1989)
Banach Center Publications
Similarity:
Cánovas, Jose S., Medina, David López (2010)
Discrete Dynamics in Nature and Society
Similarity:
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...
Jaume Llibre, Radu Saghin (2009)
Fundamenta Mathematicae
Similarity:
Let f be a continuous map on a compact connected Riemannian manifold M. There are several ways to measure the dynamical complexity of f and we discuss some of them. This survey contains some results and open questions about relationships between the topological entropy of f, the volume growth of f, the rate of growth of periodic points of f, some invariants related to exterior powers of the derivative of f, and several invariants measuring the topological complexity of f: the degree...
Šindelářová, P. (2001)
Acta Mathematica Universitatis Comenianae. New Series
Similarity:
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?
Yang, Xiao-Song, Bai, Xiaoming (2006)
Discrete Dynamics in Nature and Society
Similarity:
Michał Misiurewicz (1976)
Studia Mathematica
Similarity:
Cánovas, J.S. (2003)
Mathematica Pannonica
Similarity:
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.
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...
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.
Michał Misiurewicz (1989)
Fundamenta Mathematicae
Similarity:
Günther Palm (1975)
Publications mathématiques et informatique de Rennes
Similarity:
François Blanchard (1993)
Bulletin de la Société Mathématique de France
Similarity: