Parabolic-like maps

Details Parabolic-like maps Parabolic-like maps

2011-11-30

arxiv.org/abs/1111.7150v1

Mathematics

Dynamical Systems

34 pages, 16 figures

Scientific paper

In this paper we introduce the notion of parabolic-like mapping, which is an object similar to a polynomial-like mapping, but with a parabolic external class, i.e. an external map with a parabolic fixed point. We prove a straightening theorem for parabolic-like maps, which states that any parabolic-like map of degree 2 is hybrid conjugate to a member of the family Per_1(1), and this member is unique (up to holomorphic conjugacy) if the filled Julia set of the parabolic-like map is connected.

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