E. Fontich, R. de la Llave, P. Martin
Invariant pre-foliations for non-resonant non-uniformly hyperbolic systems
(94K, LaTeX)

ABSTRACT.  Let $\{x_i\}_{i \in \N}$ be a regular orbit of a $C^2$ 
dynamical system $f$. Let $S$ be a subset of
its Lyapunov exponents. 
Assume that all the Lyapunov exponents in $S$ 
are negative and that 
the sums of Lyapunov exponents in $S$ 
do not agree with any Lyapunov exponent in the complement
of $S$. 
Denote by $E^S_{x_i}$ the linear spaces spanned by the 
spaces associated to the Lyapunov exponents in $S$. 
We show that there are smooth manifolds $W^S_{x_i}$ such that 
$f(W^S_{x_i}) \subset W^S_{x_{i+1}}$ and $T_{x_i} W^S_{x_i} = E^S_{x_i}$. 
We establish the same  results for orbits satisfying dichotomies 
and whose rates of growth satisfy similar non-resonance conditions. 
These systems of invariant manifolds are, in general,  not a foliation.