# hyperbolic set

## Primary tabs

Synonym:
hyperbolic structure, uniformly hyperbolic
Type of Math Object:
Definition
Major Section:
Reference

## Mathematics Subject Classification

37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)

### anoteher PM article on same topic

It appears that PM has another article on the same topic

http://planetmath.org/?op=getobj&from=objects&id=3315

perhaps these should be merged??

### Re: anoteher PM article on same topic

It's not on the same topic.
For startes, my article is a definition, while the other is a theorem.
This one is about diffeomorphisms, and the other about flows.
My definition is about hyperbolic structure on invariant subsets, and the theorem in the other entry is about existence of stable/unstable manifolds for singularities of flows.

### Re: anoteher PM article on same topic

OK, whatever, as you please. Its just that flows are usually diffeomorphisms, and the structure fo the stable/unstable manifolds often are hyperbolic; the geodesic and horocycle flows being the classic textbook examples. It just seemed to me that a unified presentation of the topic would be more enlightening than a set of random disconnected factoids, neither the one article mentioning the other, or v.v. As a minimum, it might be nice to at least have a "see also" section in each artcle.

### Re: anoteher PM article on same topic

>OK, whatever, as you please. Its just that flows are usually >diffeomorphisms, and the structure fo the stable/unstable manifolds >often are hyperbolic;

I'm not sure what you mean by "flows are usually diffeomorphisms" (they are not) and by the hyperbolic structure either.

Nor I understand how the geodesic flow being (in some cases) hyperbolic is related to the stable manifold theorem for fixed points of flows (the other entry in question) or to the definition of hyperbolic set for diffeomorphisms (if you want me to mention the analogous definition for flows in my entry, you could request that by filing an addendum)

The two entries do not fit well together, and they should not be merged just because they belong to the same sub-area of mathematics.