5
votes
0answers
69 views

Short examples that are/are not quantum-ergodic

Are there any considerably short examples of manifolds that are/aren't quantum ergodic, or quantum unique ergodic? Note that a (compact) Riemannian manifold is said to be quantum ergodic if ...
7
votes
2answers
472 views

Reference request: Geodesic flow on a manifold with negative curvature is ergodic

I'm reading about the Mostow's rigidity theorem, and the proof uses the following (maybe well-known) result: The geodesic flow on a manifold with negative curvature is ergodic. The lecture note that ...
9
votes
0answers
359 views

Poincaré recurrence and symplectic packings

Question. Is there any example of a path connected symplectic manifold $(M,\omega)$ that has infinite volume, but which cannot be packed by an infinite number of symplectic balls of a fixed radius ...
6
votes
1answer
266 views

Ruelle inequality on a noncompact space

Does someone have a reference where the Ruelle inequality would be proved in the following context. Let $M$ be a non compact smooth manifold, and $f:M\to M$ be a $C^1$-diffeomorphism (or $C^2$, ...
4
votes
0answers
198 views

links and interactions between different approaches to (super-)rigidity

By super-rigidity I mean some theorems concerning the arithmetic subgroups in semi-simple Lie groups. According to Margulis "Discrete subgroups of semi-simple Lie groups" (the book published by ...
8
votes
5answers
809 views

What are the zero entropy invariant measures for an Anosov geodesic flow?

Let $M$ be the double-torus with a hyperbolic Riemannian metric. The geodesic flow on the unit tangent bundle $T^1M$ has many invariant Borel probability measures. In particular there are closed ...
5
votes
4answers
481 views

When is there a natural Riemannian metric whose measure preserves a self-diffeomorphism?

Let $M$ be a compact Riemannian manifold with metric $g$ and let $f \in Diff(M)$. Under what circumstances is there a natural metric $g_f$ s.t. the associated smooth measure $\nu_f$ is preserved by ...