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CHAOS ON ONE-DIMENSIONAL COMPACT METRIC SPACES

ZDENĚK KOČAN

Mathematical Institute in Opava, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava, Czech Republic

https://doi.org/10.1142/S0218127412502598Cited by:12 (Source: Crossref)

Abstract

We consider various kinds of chaotic behavior of continuous maps on compact metric spaces: the positivity of topological entropy, the existence of a horseshoe, the existence of a homoclinic trajectory (or perhaps, an eventually periodic homoclinic trajectory), three levels of Li–Yorke chaos, three levels of ω-chaos and distributional chaos of type 1. The relations between these properties are known when the space is an interval. We survey the known results in the case of trees, graphs and dendrites.

Keywords:

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