2019/02/25 by Bera, Sayani
#32F45 #32Q45 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1902.09369
The purpose of this note is to explore further the rigidity properties of Hénon maps from arXiv:1806.08189. For instance, we show that if H and F are Hénon maps with the same Green measure (μH=μF), or the same filled Julia set (KH=KF), or the same Green function (GH=GF), then H2 and F2 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 Hénon map H to its Green measure μH or to its filled Julia set KH or to its Green function GH is locally injective.