Carregant...
Fitxers
Tipus de document
ArticleVersió
Versió publicadaData de publicació
Tots els drets reservats
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/7785
Invariant pre-foliations for non-resonant non-uniformly hyperbolic systems
Títol de la revista
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
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.
Citació
Citació
FONTICH, Ernest, LLAVE, Rafael de la, MARTÍN, Pau. Invariant pre-foliations for non-resonant non-uniformly hyperbolic systems. _Transactions of the American Mathematical Society_. 2005. Vol. 358, núm. 3, pàgs. 1317-1345. [consulta: 31 de gener de 2026]. ISSN: 1088-6850. [Disponible a: https://hdl.handle.net/2445/7785]