 03175 E. Fontich, R. de la Llave, P. Martin
 Invariant prefoliations for nonresonant nonuniformly hyperbolic systems
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Apr 15, 03

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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 nonresonance conditions.
These systems of invariant manifolds are, in general, not a foliation.
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