Topological entropy for multidimensional perturbations of snap-back repellers and one-dimensional maps

Ming-Chia Li*, Ming Jiea Lyu, Piotr Zgliczyński

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We consider a one-parameter family of maps Fλ on with the singular map F0 having one of the two forms (i) F0(x, y) = (f(x), g(x)), where and are continuous, and (ii) F0(x, y) = (f(x), g(x, y)), where and are continuous and g is locally trapping along the second variable y. We show that if f is one-dimensional and has a positive topological entropy, or if f is high-dimensional and has a snap-back repeller, then F λ has a positive topological entropy for all λ close enough to 0.

Original languageEnglish
Pages (from-to)2555-2567
Number of pages13
JournalNonlinearity
Volume21
Issue number11
DOIs
StatePublished - 1 Nov 2008

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