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Computing explicitly topological sequence entropy: the unimodal case

Victor Jiménez López, Jose Salvador Cánovas Peña (2002)

Annales de l’institut Fourier

Let W ( I ) denote the family of continuous maps f from an interval I = [ a , b ] into itself such that (1) f ( a ) = f ( b ) ∈ { a , b } ; (2) they consist of two monotone pieces; and (3) they have periodic points of periods exactly all powers of 2 . The main aim of this paper is to compute explicitly the topological sequence entropy h D ( f ) of any map f ∈ W ( I ) respect to the sequence D = ( 2 m - 1 ) m = 1 ∞ .

Computing homology.

Kaczynski, Tomasz, Mischaikow, Konstantin, Mrozek, Marian (2003)

Homology, Homotopy and Applications

Concave iteration semigroups of linear set-valued functions

Jolanta Olko (1999)

Annales Polonici Mathematici

We consider a concave iteration semigroup of linear continuous set-valued functions defined on a closed convex cone in a separable Banach space. We prove that such an iteration semigroup has a selection which is also an iteration semigroup of linear continuous functions. Moreover it is majorized by an "exponential" family of linear continuous set-valued functions.

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