A new proof of the Stable Manifold Theorem for hyperbolic fixed points on surfaces

Details A new proof of the Stable Manifold Theorem for hyperbolic fixed points on surfaces A new proof of the Stable Manifold Theorem for hyperbolic fixed points on surfaces

2003-01-21

arxiv.org/abs/math/0301235v1

Mathematics

Dynamical Systems

1 Figure

Scientific paper

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.

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