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Properties of Dynamical Systems on Dendrites and Graphs

Zdeněk Kočan

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

E-mail Address: Zdenek.Kocan@math.slu.cz

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Veronika Kurková

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

E-mail Address: Veronika.Kurkova@math.slu.cz

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Michal Málek

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

E-mail Address: Michal.Malek@math.slu.cz

Corresponding author.

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https://doi.org/10.1142/S0218127421501005Cited by:1 (Source: Crossref)

Abstract

Dynamical systems generated by continuous maps on compact metric spaces can have various properties, e.g. the existence of an arc horseshoe, the positivity of topological entropy, the existence of a homoclinic trajectory, the existence of an omega-limit set containing two minimal sets and other. In [Kočan et al., 2014] we consider six such properties and survey the relations among them for the cases of graph maps, dendrite maps and maps on compact metric spaces.

In this paper, we consider fourteen such properties, provide new results and survey all the relations among the properties for the case of graph maps and all known relations for the case of dendrite maps. We formulate some open problems at the end of the paper.

Keywords:

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