2022
DOI: 10.1088/1361-6544/ac4b3a
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Quasi-graphs, zero entropy and measures with discrete spectrum

Abstract: In this paper, we study dynamics of maps on quasi-graphs and characterise their invariant measures. In particular, we prove that every invariant measure of a quasi-graph map with zero topological entropy has discrete spectrum. Additionally, we obtain an analog of Llibre–Misiurewicz’s result relating positive topological entropy with existence of topological horseshoes. We also study dynamics on dendrites and show that if a continuous map on a dendrite whose set of all endpoints is closed and has only finitely … Show more

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Cited by 5 publications
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References 33 publications
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