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Results tagged with ergodic-theory
Search options questions only
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user 18191
Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
13
votes
1
answer
2k
views
System with invariant measure, but no ergodic measure.
Question
Examples of continuous transformations $T: X \to X$ such that the family of invariant probability measures $M(T)$ is NOT empty but there is no ergodic measure ($E(T) = \emptyset$).
Notice t …
- 568
12
votes
3
answers
1k
views
Supremum amongst Kolmogorov-Sinai entropies: ergodic or just invariant measures.
Cases where
$sup_{\mu \in E(T)} h_\mu(T)
\neq
\sup_{\mu \in M(T)} h_\mu(T)$.
Background
For a topological space $X$,
let $T: X \to X$ be a continuous application.
Then, call the set of $T$-invarian …
- 568
5
votes
1
answer
671
views
Furstenberg-Zimmer theorem: non-invertible systems
Questions
Is there a version of the Furstenberg-Zimmer Theorem for
non-invertible measure preserving systems?
Where can I find it?
What is the precise statement?
Background
In many works that ref …
- 568
3
votes
1
answer
316
views
Compact group extension of a zero entropy system.
Suppose $T: X \to X$ is a continuous map
and $\mu$ a $T$-ergodic probability measure over the
Borel sets of $X$.
Now, suppose $K \subset \mathrm{Hom}(X)$ is a compact group
of measure-preserving homeo …
- 568