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The structures of pointwise recurrent quasi-graph maps

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arxiv 2211.07905 v1 pith:3EDUOEHA submitted 2022-11-15 math.DS

classification math.DS
keywords pointwisequasi-graphrecurrentcircleclosedconjugatecontinuouscurve
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abstract

We show that a continuous map $f$ from a quasi-graph $G$ to itself is pointwise recurrent if and only if one of the following two statements holds: (1) $X$ is a simple closed curve and $f$ is topologically conjugate to an irrational rotation on the unit circle $\mathbb S^1$; (2) $f$ is a perodic homeomorphism.

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