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Title: Invariant pre-foliations for non-resonant non-uniformly hyperbolic systems
Author: Fontich, Ernest, 1955-
Llave, Rafael de la
Martín, Pau
Keywords: Sistemes dinàmics diferenciables
Teories no lineals
Dynamical systems with hyperbolic behavior
Invariant manifold theory
Nonlinear dynamics
Issue Date: 2005
Publisher: American Mathematical Society
Abstract: Given an orbit whose linearization has invariant subspaces satisfying some non-resonance conditions in the exponential rates of growth, we prove existence of invariant manifolds tangent to these subspaces. The exponential rates of growth can be understood either in the sense of Lyapunov exponents or in the sense of exponential dichotomies. These manifolds can correspond to "slow manifolds", which characterize the asymptotic convergence. Let {x i } i∈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 xi the linear spaces spanned by the spaces associated to the Lyapunov exponents in S. We show that there are smooth manifolds W S xi such that f(W S xi ) ⊂ W S xi+1 and T xi W S xi = E S xi . 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 not, in general, a foliation.
Note: Reproducció digital del document publicat en format paper, proporcionada per JSTOR
It is part of: Transactions of the American Mathematical Society, 2005, vol. 358, núm. 3, p. 1317-1345.
ISSN: 1088-6850
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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