Decomposition of rational maps

Mikhail Hlushchanka
University of California, Los Angeles
https://sites.google.com/site/mikhailhlushchanka/

Date(s) : 26/03/2021   iCal
11 h 00 min - 12 h 00 min

There are various classical and more recent decomposition results in mapping class group theory, geometric group theory, and complex dynamics (which include celebrated results by Bill Thurston). The goal of this talk is to introduce a new decomposition of rational maps based on the geometry of their Julia sets. Namely, we will discuss the following result: every postcritically-finite rational map with non-empty Fatou set can be canonically decomposed into crochet maps (these have “very thinly connected Julia sets”) and Sierpinski carpet maps (these have “very heavily connected Julia sets”).
Based on joint work with Dima Dudko and Dierk Schleicher.

Lien Zoom :

Decomposition of rational maps (tuning) in
D. Dudko, M. Hlushchanka, D. Schleicher,
Decomposition theory of postcritically-finite rational maps
and its applications (paper in preparation).

Emplacement
FRUMAM, St Charles (2ème étage)

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