Invariant manifolds near hyperbolic fixed points

Abstract

In these notes, we discuss obstructions to the existence of local invariant manifolds of some smoothness class, near hyperbolic fixed points of diffeomorphisms. We present an elementary construction for continuously differentiable invariant manifolds that are not necessarily normally hyperbolic, near attracting fixed points. The analogous theory for invariant manifold near hyperbolic equilibria of differential equations is included. For differential equations, we construct one dimensional invariant manifolds of higher smoothness class.

Keywords:

• Hyperbolic fixed points
• Smoothness
• Diffeomorphisms
• Differential equations