Invariant graphs of rational maps

Guizhen Cui; Jinsong Zeng; Yan Gao

Invariant graphs of rational maps

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arxiv 1907.02870 v2 pith:HZRX2R5K submitted 2019-07-05 math.DS

Guizhen Cui , Yan Gao , Jinsong Zeng This is my paper · ORCID

classification math.DS

keywords finiteinvariantrationalconnectedcontainsenoughexistsgraph

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abstract

Let $f$ be a postcritically finite rational map. We prove that, as $n$ large enough, there exists an $f^n$-invariant (finite connected) graph on $\widehat{\mathbb{C}}$ such that it contains the postcritical set of $f$.

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