A new proof of the stable manifold theorem for hyperbolic fixed points on surfaces

Abstract

We introduce a new technique for proving the classical stable manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the convergence of a canonical sequence of “finite time local stable manifolds” which are related to the dynamics of a finite number of iterations.

Keywords:

• Stable manifold theorem
• Hyperbolic fixed point
• Canonical sequence
• Local stable manifolds
• Primary [2000] 37D10

Acknowledgements

In writing this article, the authors acknowledge the support of the EPSRC, grant no. GR/S11862/01.

Notes

§[email protected]; URL: www.ma.ic.ac.uk/~luzzatto

Additional information

Notes on contributors

Stefano Luzzatto §

§[email protected]; URL: www.ma.ic.ac.uk/~luzzatto