Approximating entropy of maps of the interval
Louis Block, Ethan M. Coven (1989)
Banach Center Publications
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Louis Block, Ethan M. Coven (1989)
Banach Center Publications
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Cánovas, Jose S., Medina, David López (2010)
Discrete Dynamics in Nature and Society
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Šindelářová, P. (2001)
Acta Mathematica Universitatis Comenianae. New Series
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François Blanchard (1993)
Bulletin de la Société Mathématique de France
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Yang, Xiao-Song, Bai, Xiaoming (2006)
Discrete Dynamics in Nature and Society
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Cánovas, J.S. (2003)
Mathematica Pannonica
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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...
Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Coven, E.M., Smítal, J. (1993)
Acta Mathematica Universitatis Comenianae. New Series
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Inder Jeet Taneja (1977)
Annales Polonici Mathematici
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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...
Riečan, B.
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Dawid Huczek (2012)
Colloquium Mathematicae
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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.
Jozef Bobok (2002)
Studia Mathematica
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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?
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.