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On the Stable Manifold Theorem Alberto Abbondandolo, Pietro Majer
 

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 TxM = Es
Eu
such that, for some equivalent norm | | on TxM,
|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