03-175 E. Fontich, R. de la Llave, P. Martin

Invariant pre-foliations for non-resonant non-uniformly hyperbolic systems (94K, LaTeX) Apr 15, 03

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 03-175.tex