Basic Dynamical Stability Results for P
نویسنده
چکیده
We study stability questions for dynamics on Pn. To do so we use locally simply parameterized holomorphic families. We prove a weak version of the λ-lemma for dynamical systems on Pn. This takes the form of showing that the set of potential traces for a holomorphic motion that preserve the dynamics (i.e. the set of “Fatou sections”) is compact. We introduce the notion of a postcritically bounded holomorphic family and show that if a (locally simply parameterized) holomorphic family is postcritically bounded by some open subset of Pn then: (1) repelling periodic points in the Julia set for one member of the family can not bifurcate, nor can they leave the Julia set in other members
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تاریخ انتشار 2002