Hyperbolicity via Evolution Semigroups on L p

• Autores: Luis Barreira, Claudia Valls
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 3, 2019, págs. 887-908
• Idioma: inglés
• DOI: 10.1007/s12346-019-00318-8
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• Resumen

  • For a measurable cocycle over a measurable flow with values on a Banach space, we give a complete characterization of its nonuniform hyperbolicity in terms of an evolution semigroup on Lp. We consider the general cases of a space Lp determined by a Borel measure that need not be invariant and of an evolution semigroup that need not be strongly continuous, which makes it impossible to use generators. A nontrivial application of our work is the robustness of the hyperbolicity, either uniform or nonuniform, for measurable cocycles over a measurable flow: namely, the robustness of the hyperbolicity for the evolution semigroup yields the robustness of the hyperbolicity for the corresponding cocycle.