[Todos CMAT] Seminario de Sistemas Dinámicos - Maik Gröger (Jagiellonian University)

[seminarios en cmat.edu.uy]

Seminario de Sistemas Dinámicos
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Título: "Continuity of Følner averages"

Expositor: Maik Gröger (Jagiellonian University)

Resumen:
 
The notion of generic/mean points goes back to the seminal work of Krylov and
Bogolyubov.   The first to investigate the question of what happens when all
points of a dynamical   system are generic for some invariant measure seem to be
Dowker and Lederer in 1964.   As it turns out, combining this property with
other topological regularity   criteria yields measure-theoretic rigidity
results of the dynamical system.   For example, minimality of the system implies
its unique ergodicity in this setting.   Another natural topological criterion
in place of minimality is to assume that   the map, which assigns each point its
invariant measure to which it is generic, is continuous.   By several recent
works by different authors, the following picture emerges for   abelian group
actions in this setting: each point is generic for some ergodic measure   and
even stronger, each orbit closure is uniquely ergodic.   In my talk, I will show
that this is no longer the case for general actions by   topological amenable
groups, providing concrete counter-examples involving the group of   all
orientation preserving homeomorphisms on the unit interval as well as the
Lamplighter group.   Moreover, in the course of the talk I will elaborate on the
recently introduced notion   of weak mean equicontinuity if time permits.

This is joint work with G. Fuhrmann and T. Hauser.
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Viernes 24/2 a las 14:30, Salón de seminarios del IMERL

Contacto: Santiago Martinchich - smartinchich en cmat.edu.uy
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Próxima semana: Sesión doble el lunes y escuela ''Topics on the geometry of
locally symmetric spaces'' a partir del martes.
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Más seminarios en: http://www.cmat.edu.uy/seminarios
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