Computing explicitly topological sequence entropy: the unimodal case

Victor Jiménez López[1]; Jose Salvador Cánovas Peña[2]

  • [1] Universidad de Murcia, Departamento de Matemáticas, Campus de Espinardo, 30100 Murcia (Espagne)
  • [2] Universidad Politécnica de Cartagena, Departamento de Matemática Aplicada, Paseo de Alfonso XIII 34-36, 30203 Cartagena (Espagne)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 4, page 1093-1133
  • ISSN: 0373-0956

Abstract

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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 ∞ .

How to cite

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Jiménez López, Victor, and Cánovas Peña, Jose Salvador. "Computing explicitly topological sequence entropy: the unimodal case." Annales de l’institut Fourier 52.4 (2002): 1093-1133. <http://eudml.org/doc/116005>.

@article{JiménezLópez2002,
abstract = {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)\in \lbrace a,b\rbrace $; (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 $f\in W(I)$ respect to the sequence $D=(2^\{m-1\})_\{m=1\}^\infty $.},
affiliation = {Universidad de Murcia, Departamento de Matemáticas, Campus de Espinardo, 30100 Murcia (Espagne); Universidad Politécnica de Cartagena, Departamento de Matemática Aplicada, Paseo de Alfonso XIII 34-36, 30203 Cartagena (Espagne)},
author = {Jiménez López, Victor, Cánovas Peña, Jose Salvador},
journal = {Annales de l’institut Fourier},
keywords = {map of type $2^\infty $; topological sequence entropy; unimodal map; map of type },
language = {eng},
number = {4},
pages = {1093-1133},
publisher = {Association des Annales de l'Institut Fourier},
title = {Computing explicitly topological sequence entropy: the unimodal case},
url = {http://eudml.org/doc/116005},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Jiménez López, Victor
AU - Cánovas Peña, Jose Salvador
TI - Computing explicitly topological sequence entropy: the unimodal case
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 4
SP - 1093
EP - 1133
AB - 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)\in \lbrace a,b\rbrace $; (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 $f\in W(I)$ respect to the sequence $D=(2^{m-1})_{m=1}^\infty $.
LA - eng
KW - map of type $2^\infty $; topological sequence entropy; unimodal map; map of type
UR - http://eudml.org/doc/116005
ER -

References

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