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arXiv · 1902.09369

Rigidity Theorems for H\'{e}non maps-II

Sayani Bera
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Abstract

The purpose of this note is to explore further the rigidity properties of H\'{e}non maps from arXiv:1806.08189. For instance, we show that if $H$ and $F$ are H\'{e}non maps with the same Green measure ($\mu_H=\mu_F$), or the same filled Julia set ($K_H=K_F$), or the same Green function ($G_H=G_F$), then $H^2$ and $F^2$ have to commute. This, in turn, gives that $H$ and $F$ have the same non-escaping sets. Further we prove that, either of the association of a H\'{e}non map $H$ to its Green measure $\mu_H$ or to its filled Julia set $K_H$ or to its Green function $G_H$ is locally injective.

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Sayani Bera. 2019-02-25. Rigidity Theorems for H\'{e}non maps-II. https://arxiv.org/abs/1902.09369

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