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Displaying similar documents to “Topological sequence entropy for maps of the circle”

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.

Distributional chaos on tree maps: the star case

Jose S. Cánovas (2001)

Commentationes Mathematicae Universitatis Carolinae

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Let 𝕏 = { z : z n [ 0 , 1 ] } , n , and let f : 𝕏 𝕏 be a continuous map having the branching point fixed. We prove that f is distributionally chaotic iff the topological entropy of f is positive.