Rigidity theorems for Hénon maps—II
Tom 253 / 2021
Fundamenta Mathematicae 253 (2021), 1-16
MSC: Primary 32H50; Secondary 32H02, 37F50.
DOI: 10.4064/fm728-6-2020
Opublikowany online: 17 November 2020
Streszczenie
The purpose of this note is to explore further the rigidity properties of Hénon maps from [S. Bera et al., Eur. J. Math. 6 (2020)]. For instance, we show that if $H$ and $F$ are Hénon maps with either 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 and they share the same non-escaping sets. Further, we prove that assigning to an Hénon map $H$ its Green measure $\mu _H$, or its filled Julia set $K_H$, or its Green function $G_H$ is locally injective in the space of Hénon maps (with the topology of uniform convergence on compact sets).
