The Mandelbrot set and its satellite copies
speaker: Luna Lomonaco (IMPA)abstract: Douady and Hubbard proved the existence of homeomorphic copies of the Mandelbrot M inside of M, which can be primitive (roughly speaking the ones with a cusp) or a satellite (without a cusp). Lyubich proved that the primitive copies of M are quasiconformally homeomorphic to M, and that the satellite ones are quasiconformally homeomorphic to M outside any small neighbourhood of the root. The satellite copies are not quasiconformally homeomorphic to M (as we cannot straighten a cusp quasiconformally), and we proved in a previous work with C. Petersen that in general are not mutually quasiconformally homeomorphic. We show now that the satellite copies having rotation numbers with the same denominator are quasiconformally homeomorphic.
timetable:
Tue 28 May, 11:30 - 12:20, Aula Dini
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