[Todos CMAT] Seminario Sistemas Dinámicos

Matias Carrasco matiascapi en gmail.com
Mie Nov 4 23:16:52 UYT 2015


este viernes 6/11 a las 14:30 en el salón de seminarios del IMERL tenemos el placer de recibir a Sébastien Alvarez (IMPA).

Abajo título y resumen.


Titre: Ends, dynamics and algebraic structures of groups acting on the circle.

We study the following natural question: how does the algebraic structure of a group of diffeomorphisms of the circle affects its dynamics, and reciprocally? For example, we know since Denjoy that a cyclic group of C2 diffeomorphisms acts on the circle without an invariant Cantor set. Better: a theorem of Ghys, which relies on a work by Duminy, states that the groups of analytic diffeomorphisms with an exceptional minimal set are virtually free. A group G which admits an exceptional minimal set is discrete in a special sense: for any interval I intersecting the minimal set, the restriction of the identity to I is isolated in the C1 topology among the set of restrictions to I of
the diffeomorphisms of G.
In this talk we intend to illustrate a paradigm which appears in recents work by Deroin, Kleptsyn, Navas and Filimonov: this notion of discreteness separates groups with a simple dynamics and a well determined algebraic structure (the group is virtually free or conjugated to an extension of a Fuchsian group), from groups with a rigid yet rich dynamics.

It is a joint work with D. Filiminov (HSE Moscou), V. Kleptsyn (CNRS, Rennes), D. Malicet
(PUC), C. Meniño (PUC), A. Navas (USACH, Santiago), and M. Triestino (PUC).

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