ABSTRACT
A hyperbolic set for a diffeomorphism is an invariant set for which every point behaves like a hyperbolic fixed point. More precisely, the tangent space at each point of the invariant set splits into stable and unstable subspaces so that the derivative of the mapping takes the stable subspace at a point into the stable subspace at the image of that point, and the unstable subspace at a point into the unstable subspace at the image of that point. Moreover, the vectors in the stable subspace are uniformly contracted and the vectors in the unstable subspace are uniformly expanded by the derivative of the mapping.
