Approximability of dynamical systems between trees of spheres

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We study sequences of analytic conjugacy classes of rational maps that diverge in moduli space. In particular, we are interested in the notion of rescaling limits introduced by Jan Kiwi. From [A1], we recall the notion of dynamical covers between trees of spheres for which a periodic sphere corresponds to a rescaling limit. We study necessary conditions for such a dynamical cover to be the limit of dynamically marked rational maps. With these conditions, we classify these covers in the case of bi-critical maps, and we recover the second main result of Jan Kiwi regarding rescaling limits.

Original languageEnglish
Pages (from-to)1945-1977
Number of pages33
JournalIndiana University Mathematics Journal
Issue number6
StatePublished - 2016


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