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Results tagged with ergodic-theory
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user 18698
Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
10
votes
2
answers
470
views
When is every orbit closure uniquely ergodic?
Given a topological dynamical system $(X,T)$ (so that $T$ is a homeomorphism of the compact metric space $X$) and a point $x\in X$ we call the set ${\mathcal O}(x):=\overline{\{T^nx:n\in\mathbb Z\}}$ …
- 1,701
7
votes
1
answer
553
views
Failure of the Pointwise Ergodic Theorem
It is known that Birkhoff's pointwise ergodic theorem (unlike von Neumann's mean ergodic Theorem) fails to hold for general Folner sequences.
The counter-example usually given is the Folner sequence …
- 1,701
5
votes
Accepted
Are irrational multiples of central sets again central?
The answer is yes, it was pointed out to me by Vitaly Bergelson that it follows from Theorem 6.1 (d) of a paper by Bergelson, Hindman and Kra (Trans. Amer. Math. Soc. 348 (1996), no. 3, 893–912).
The …
- 1,701