Topological and Combinatorial Problems in One-dimensional Complex Dynamics

Rescaling limits of quadratic Blaschke products

speaker: Adam Epstein (University of Warwick)

abstract: Let $f_k$ be a sequence of quadratic rational maps diverging in moduli space. Under certain circumstances, there may exist a sequence of conjugate maps $F_k$ and some $q\geq 2$ such that the iterates $F_k^q$ converge algebraically to a rational map of degree 2 or more. It has been conjectured that, up to a suitable notion of equivalence, there can be at most two such {\em rescaling limits}, the first a quadratic rational map with a fixed point of multiplier 1, the second a quadratic polynomial. We focus on the first rescaling limit, with attention to the special case of Blaschke products. The second rescaling limit will be discussed in the talk of Petersen, with whom this project is joint work.

timetable:
Fri 18 Oct, 9:00 - 10:00, Aula Dini
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