On topological sequence entropy and chaotic maps on inverse limit spaces
Author
Cánovas Peña, José SalvadorKnowledge Area
Matemática AplicadaSponsors
This paper has been partially supported by the grant PB/2/FS/97 (Fundación Séneca, Comunidad Autónoma de Murcia). I wish to thank the referee for the proof of Proposition 2.1 and the comments that helped me to improve the paper.Publication date
1999Publisher
Institute of Applied Mathematics Faculty of Mathematics, Physics and Informatics Comenius UniversityBibliographic Citation
CANOVAS, J.S. On topological sequence entropy and chaotic maps on inverse limit spaces. Acta Mathematica Universitatis Comenianae, LXVIII (2): 205-211, 1999. ISSN 0862-9544Keywords
Secuencia de Entropía topológicaMapa caótico
Entropía topológica
Caos
Topological sequence entropy
Chaotic maps
Chaos
Topological Entropy
Abstract
The aim of this paper is to prove the following results: a continuous
map f : [0; 1] ! [0; 1] is chaotic if the shift map of : lim
([0; 1]; f) ! lim
([0; 1]; f) is
chaotic. However, this result fails, in general, for arbitrary compact metric spaces.
f : lim
([0; 1]; f) ! lim
([0; 1]; f) is chaotic i there exists an increasing sequence
of positive integers A such that the topological sequence entropy hA( f ) > 0. Finally,
for any A there exists a chaotic continuous map fA : [0; 1] ! [0; 1] such that
hA( fA) = 0:
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