On topological sequence entropy and chaotic maps on inverse limit spaces
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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.Fecha de publicación
1999Editorial
Institute of Applied Mathematics Faculty of Mathematics, Physics and Informatics Comenius UniversityCita bibliográfica
CANOVAS, J.S. On topological sequence entropy and chaotic maps on inverse limit spaces. Acta Mathematica Universitatis Comenianae, LXVIII (2): 205-211, 1999. ISSN 0862-9544Palabras clave
Secuencia de Entropía topológicaMapa caótico
Entropía topológica
Caos
Topological sequence entropy
Chaotic maps
Chaos
Topological Entropy
Resumen
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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