Computing explicitly topological sequence entropy: the unimodal case

Victor Jiménez López; Jose Salvador Cánovas Peña

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Commutativity and non-commutativity of topological sequence entropy

Francisco Balibrea, Jose Salvador Cánovas Peña, Víctor Jiménez López (1999)

Annales de l'institut Fourier

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In this paper we study the commutativity property for topological sequence entropy. We prove that if $X$ is a compact metric space and $f, g : X \to X$ are continuous maps then $h_{A} (f \circ g) = h_{A} (g \circ f)$ for every increasing sequence $A$ if $X = [0, 1]$ , and construct a counterexample for the general case. In the interim, we also show that the equality $h_{A} (f) = h_{A} (f |_{\cap_{n \geq 0} f^{n} (X)})$ is true if $X = [0, 1]$ but does not necessarily hold if $X$ is an arbitrary compact metric space.

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Michał Misiurewicz (1989)

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Anna Zdunik (1984)

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Mariusz Lemańczyk (1985)

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Sequence entropy pairs and complexity pairs for a measure

Wen Huang, Alejandro Maass, Xiangdong Ye (2004)

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In this paper we explore topological factors in between the Kronecker factor and the maximal equicontinuous factor of a system. For this purpose we introduce the concept of sequence entropy $n$ -tuple for a measure and we show that the set of sequence entropy tuples for a measure is contained in the set of topological sequence entropy tuples [H- Y]. The reciprocal is not true. In addition, following topological ideas in [BHM], we introduce a weak notion and a strong notion of complexity...

The topological entropy versus level sets for interval maps

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?

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Kneading sequences of skew tent maps

M. Misiurewicz, E. Visinescu (1991)

Annales de l'I.H.P. Probabilités et statistiques

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