homoclinic class
Let be a compact smooth manifold
and a diffeomorphism. The homoclinic class of a hyperbolic periodic point
of , denoted , is the closure
of the set of transverse intersections
between the stable and unstable manifolds all points in the orbit of ; i.e.
Homoclinic classes are topologically transitive, and the number of homoclinic classes is at most countable. Moreover, generically (in the topology
of ), they are pairwise disjoint and maximally transitive
.
Title | homoclinic class |
---|---|
Canonical name | HomoclinicClass |
Date of creation | 2013-03-22 14:07:30 |
Last modified on | 2013-03-22 14:07:30 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 6 |
Author | Koro (127) |
Entry type | Definition |
Classification | msc 37C29 |