Parabolic-like mappings
speaker: Luna Lomonaco (IMPA)abstract: A polynomial-like mapping is a proper holomorphic map $f : U' \rightarrow U$, where $U',\,\, U \approx \D$, and $U'\subset \subset U$. This definition captures the behaviour of a polynomial in a neighbourhood of its filled Julia set. A polynomial-like map of degree $d$ is determined up to holomorphic conjugacy by its internal and external classes, that is, the (conjugacy classes of) the restrictions to the filled Julia set and its complement. In particular the external class is a degree $d$ real-analytic orientation preserving and strictly expanding self-covering of the unit circle: the expansivity of such a circle map implies that all the periodic points are repelling, and in particular not parabolic.
We extended the polynomial-like theory to a class of parabolic mappings which we called parabolic-like mappings. A parabolic-like mapping is thus similar to a polynomial-like mapping, but with a parabolic external class; that is to say, the external map has a parabolic fixed point, whence the domain is not contained in the codomain.
timetable:
Mon 14 Oct, 16:45 - 17:15, Aula Dini
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