[Todos CMAT] Seminario Sistemas Dinámicos

Matias Carrasco matiascapi en gmail.com
Mie Feb 17 15:48:51 UYT 2016


Buenas,

este viernes 19/2 a las 14:00 en el salón de seminarios del IMERL tenemos
el placer de escuchar a Luna Lomonaco (San Pablo).

Abajo título y resumen.

AVISO: El calendario del seminario está casi libre para este semestre. Si
tienen invitados o quieren hablar, no duden en avisar.

Saludos

Matías

Titulo: 'On quasiconformal (in)-compatibility of satellite copies of the
Mandelbrot set'

Abstract: For a polynomial on the Riemann sphere, infinity is a (super)
attracting fixed point, and the filled Julia set is the set of points with
bounded orbit. Consider the quadratic family P_c(z)=z^2+c. The Mandelbrot
set M  is the set of parameters c such that the filled Julia set of P_c is
connected. Douady and Hubbard, using renormalization, proved the existence
of homeomorphic copies of M inside of M, which can be primitive (if,
roughly speaking, they have a cusp) or satellite (if they don't). They
conjectured that the primitive copies of M are quasiconformal homeomorphic
to M, and that the satellite ones are quasiconformal homeomorphic to M
outside any small neighbourhood of the root. These results are now theorems
due to Lyubich. The satellite copies are not quasiconformal homeomorphic to
M, but are they mutually quasiconformally homeomorphic? In a joint work
with C. Petersen we prove that this question, which has been open for about
20 years, has in general a negative answer.
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