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Results tagged with ergodic-theory
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user 9095
Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
5
votes
On The Convergence of Ergodic Measures
consider the torus map $(x,y) \mapsto (x+y, y)$. For every $y$, this gives a rotation on the circle $S^1 \times y$. That is, Lebesgue measure on any "horizontal" circle is preserved. For $y$ rational …
- 2,244
2
votes
When is there a natural Riemannian metric whose measure preserves a self-diffeomorphism?
Right, so your question really is: what diffeos preserve a measure equivalent to the volume (ok, with smooth Radon Nikodym derivative, if you're talking smooth metrics). This is because any volume for …
- 71