Minimal Self-Joinings and Positive Topological Entropy.
F. Blanchard, E. Glasner (1995)
Monatshefte für Mathematik
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F. Blanchard, E. Glasner (1995)
Monatshefte für Mathematik
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N. Yanagihara, Shin Kawase (1974)
Monatshefte für Mathematik
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Brian Marcus (1979)
Monatshefte für Mathematik
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Bodo Volkmann, Anne Bertrand-Mathis (1989)
Monatshefte für Mathematik
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Gilbert Helmberg (1982)
Monatshefte für Mathematik
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Nobua Aoki (1979)
Monatshefte für Mathematik
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Paul C. Shields, Robert M. Burton (1983)
Monatshefte für Mathematik
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Manfred Denker (1979)
Monatshefte für Mathematik
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Nikita Sidorov, Anatoly Vershik (1998)
Monatshefte für Mathematik
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Michał Misiurewicz (1976)
Studia Mathematica
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F. Benatti, H. Narnhofer (1997)
Monatshefte für Mathematik
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Qing Zhang, Thomas Ward (1992)
Monatshefte für Mathematik
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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...
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?
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...