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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/7785
Invariant pre-foliations for non-resonant non-uniformly hyperbolic systems
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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.
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FONTICH, Ernest, LLAVE, Rafael de la and MARTÍN, Pau. Invariant pre-foliations for non-resonant non-uniformly hyperbolic systems. Transactions of the American Mathematical Society. 2005. Vol. 358, num. 3, pags. 1317-1345. ISSN 1088-6850. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/7785