|24 III||Dominik Kwietniak (Jagiellonian University)|
Choquet simplices as spaces of invariant probability
Many examples illustrating the limitations of the dynamical systems theory are
defined on quite exotic spaces. We also know that the geometry of
manifolds severely restricts available dynamics. On the other hand, physically
relevant models of real-life phenomena result in smooth dynamical systems acting
on manifolds. These observations are behind one of the most intriguing questions
in the dynamical systems theory: given a property P that a dynamical system
may or may not have, and a family C of dynamical systems decide whether a
system exhibiting P exists in C. A very famous instance of that question is the
smooth realisation problem. It asks if every measure preserving system
to a system given by a smooth diffeomorphism of a compact manifold preserving
a measure equivalent to the volume element. The question is inspired by a brief
remark made in 1932 by Johnny von Neumann in his foundational paper on ergodic
theory and remains unresolved.
During my talk, I will discuss the recent progress on the following variant of
the realisation problem: which nonempty Choquet simplices can be realised as
simplices of invariant measures for minimal homeomorphisms on manifolds.
(joint work with Sejal Babel, Jernej Cinc, Till Hauser, Piotr Oprocha)
no result found, sorry.
The seminar takes place on Fridays
at 10.15-11.45 AM (Kraków time) - currently CEST (UTC+2) in the room 1016
of the Jagiellonian University
Department of Mathematics
and Computer Science
(ul. Łojasiewicza 6, Cracow).