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.
|Date of creation||2013-03-22 14:07:30|
|Last modified on||2013-03-22 14:07:30|
|Last modified by||Koro (127)|