Summary: On the Stable Manifold Theorem
Alberto Abbondandolo, Pietro Majer
January 2001
Let M be a manifold of class Cr
, 1 r or r = (as usual, C
denotes the analytic
category), modeled on the Banach space E. Let f : M M be a Cr
diffeomorphism. Assume
that ¯x is a hyperbolic fixed point of f, meaning that f(¯x) = ¯x and that there is a Df(¯x)-invariant
splitting T¯xM = Es
Eu
such that, for some equivalent norm | · | on T¯xM,
|Df(¯x)| || if Es
, |Df(¯x)|
1

|| if Eu
,
for some ]0, 1[. The definition of hyperbolicity and the subspaces Es
, Eu

Source: Abbondandolo, Alberto - Scuola Normale Superiore of Pisa

Collections: Mathematics