Rigidity of hyperbolic sets on surfaces. (English) Zbl 1173.37317
Summary: Given a hyperbolic invariant set of a diffeomorphism on a surface, it is proved that, if the holonomies are sufficiently smooth, then the diffeomorphism on the hyperbolic invariant set is rigid in the sense that it is \(C^{1+}\) conjugate to a hyperbolic affine model.
MSC:
| 37D20 | Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) |
| 37E30 | Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces |
