Rigidity theorems for Hénon maps—II
Tom 253 / 2021
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 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).