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Category Archives: topological dynamics
A useful example for the space of ergodic measures
Last time I discussed the following three properties that may or may not be satisfied for a map on a compact metric space : (C) The set of ergodic measures is pathconnected. (D) is dense in the set of all … Continue reading
Some questions on ergodic measures
This post will be a brief set of notes recording some thoughts from my talk at the Penn State dynamics seminar today, since I did not produce slides but rather spoke more informally about some results I’ve recently learned (which … Continue reading
Posted in ergodic theory, topological dynamics
Tagged entropy density, Poulsen simplex, space of invariant measures
1 Comment
Specification
In the last post we saw that if is the space of invariant probability measures for the full shift, then the collection of ergodic measures (which are the extreme points of the simplex ) has two remarkable properties: is dense … Continue reading
Notions of irreducibility
Let be a topological dynamical system. (Generally this means, for me at least, a continuous selfmap of a compact metric space. However, sometimes one may be interested in examples that are not compact or that are only piecewise continuous.) We … Continue reading
Posted in ergodic theory, topological dynamics
Tagged Poulsen simplex, space of invariant measures
3 Comments