Let be a compact smooth manifold, and let be a diffeomorphism. An -invariant subset of is said to be hyperbolic (or to have an hyperbolic structure) if there is a splitting of the tangent bundle of restricted to into a (Whitney) sum of two -invariant subbundles, and such that the restriction of is a contraction and is an expansion. This means that there are constants and such that
and for each ;
for each and ;
for each and .
using some Riemannian metric on .
If is hyperbolic, then there exists an adapted Riemannian metric, i.e. one such that .
|Date of creation||2013-03-22 13:40:21|
|Last modified on||2013-03-22 13:40:21|
|Last modified by||Koro (127)|