Displaying similar documents to “Computing explicitly topological sequence entropy: the unimodal case”

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 → X are continuous maps then h A ( f ∘ g ) = h A ( g ∘ 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 | ∩ n ≥ 0 f n ( X ) ) is true if X = [ 0 , 1 ] but does not necessarily hold if X is an arbitrary compact metric space.

Sequence entropy pairs and complexity pairs for a measure

Wen Huang, Alejandro Maass, Xiangdong Ye (2004)

Annales de l’institut Fourier

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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?