# Tag Info

Accepted

### Ergodicity and mixing of geodesic and horocyclic flows

The algebraic approach is just one of many ways to deal with the geodesic and horocycle flows. Also your quick summary does not really pay tribute to the many ways to deal with it using "...
• 18.6k
Accepted

### How to find the hyperbolic dimension of map $f(z) = z^2$ of $\overline{\mathbb{C}}$ onto itself?

The hyperbolic dimension of $f$ is 1 and its maximal hyperbolic set is the unit circle $\mathbb{S}^1$. First we show that a hyperbolic set for $f$ must be contained in the unit circle $\mathbb{S}^1$. ...
• 657

### How can I prove that the suspension of an Anosov diffeomorphism is an Anosov flow?

The short answer, as pointed out in the comments, is that yes, contraction at regular intervals is enough, because the definition of Anosov requires that there are $C>0$ and $\lambda\in (0,1)$ such ...
• 8,752

### When entropy SRB measure is zero

The SRB measure is always isomorphic to a Bernoulli scheme (up to a period) and hence has positive entropy. Regarding continuity properties of entropy, we have upper semicontinuity whenever the map ...
• 8,752

### Can the Reeb foliation of $S^3$ be realized as stable manifold foliation of a smooth hyperbolic discrete dynamic on $S^3$?

No, because it has a unique leaf that is a torus. That can't be a stable or unstable manifold; one reason is that it can't get either bigger or smaller under the action of the hyperbolic dynamical ...
• 5,681
Accepted

### Non-absolutely continuous foliation

I don’t have the Handbook near me at the moment so I can’t look at the example you mention, but at https://vaughnclimenhaga.wordpress.com/2013/11/24/fubini-foiled/ I describe a construction of Milnor’...
• 8,752

### Canonically representing the monodromy of a hyperbolic manifold fibered over $S^1$

Here is an answer of sorts; it is not completely canonical though. First of all, you have to pick a conformal or hyperbolic structure on the fiber $\Sigma$. This can be made almost canonical, since ...
• 9,817

### Canonically representing the monodromy of a hyperbolic manifold fibered over $S^1$

The pseudo-Anosov homeomorphism is a diffeomorphism away from finitely many singular points, so in general will not be a smooth diffeomorphism. However, for certain fibered knots there are not ...
• 67.4k