Displaying similar documents to “Commutativity and non-commutativity of topological sequence entropy”

Topological sequence entropy for maps of the circle

Roman Hric (2000)

Commentationes Mathematicae Universitatis Carolinae

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A continuous map f of the interval is chaotic iff there is an increasing sequence of nonnegative integers T such that the topological sequence entropy of f relative to T , h T ( f ) , is positive ([FS]). On the other hand, for any increasing sequence of nonnegative integers T there is a chaotic map f of the interval such that h T ( f ) = 0 ([H]). We prove that the same results hold for maps of the circle. We also prove some preliminary results concerning topological sequence entropy for maps of general compact...

Computing explicitly topological sequence entropy: the unimodal case

Victor Jiménez López, Jose Salvador Cánovas Peña (2002)

Annales de l’institut Fourier

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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 .

The topological entropy versus level sets for interval maps (part II)

Jozef Bobok (2005)

Studia Mathematica

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Let f: [a,b] → [a,b] be a continuous function of the compact real interval such that (i) c a r d f - 1 ( y ) 2 for every y ∈ [a,b]; (ii) for some m ∈ ∞,2,3,... there is a countable set L ⊂ [a,b] such that c a r d f - 1 ( y ) m for every y ∈ [a,b]∖L. We show that the topological entropy of f is greater than or equal to log m. This generalizes our previous result for m = 2.

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?

Operator entropy inequalities

M. S. Moslehian, F. Mirzapour, A. Morassaei (2013)

Colloquium Mathematicae

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We investigate a notion of relative operator entropy, which develops the theory started by J. I. Fujii and E. Kamei [Math. Japonica 34 (1989), 341-348]. For two finite sequences A = (A₁,...,Aₙ) and B = (B₁,...,Bₙ) of positive operators acting on a Hilbert space, a real number q and an operator monotone function f we extend the concept of entropy by setting S q f ( A | B ) : = j = 1 n A j 1 / 2 ( A j - 1 / 2 B j A j - 1 / 2 ) q f ( A j - 1 / 2 B j A j - 1 / 2 ) A j 1 / 2 , and then give upper and lower bounds for S q f ( A | B ) as an extension of an inequality due to T. Furuta [Linear Algebra Appl. 381 (2004),...

A local approach to g -entropy

Mehdi Rahimi (2015)

Kybernetika

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In this paper, a local approach to the concept of g -entropy is presented. Applying the Choquet‘s representation Theorem, the introduced concept is stated in terms of g -entropy.

Entropies of self-mappings of topological spaces with richer structures

Miroslav Katětov (1993)

Commentationes Mathematicae Universitatis Carolinae

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For mappings f : S S , where S is a merotopic space equipped with a diameter function, we introduce and examine an entropy, called the δ -entropy. The topological entropy and the entropy of self-mappings of metric spaces are shown to be special cases of the δ -entropy. Some connections with other characteristics of self-mappings are considered. We also introduce and examine an entropy for subsets of S N , which is closely connected with the δ -entropy of f : S S .