Naslov
Admissibility and nonuniform exponential trichotomies

Autori
Barreira, Luis ; Dragičević, Davor ; Valls, Claudia

Izvornik
Regular & chaotic dynamics (1560-3547) 20 (2015), 1; 49-62

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
exponential trichotomy ; nonuniform hyperbolicity ; robustness ; partially hyperbolic set

Sažetak
For a nonautonomous dynamics defined by a sequence of linear operators acting on a Banach space, we show that the notion of a nonuniform exponential trichotomy can be completely characterized in terms of admissibility properties. This refers to the existence of bounded solutions under any bounded time- dependent perturbation of certain homotheties of the original dynamics. We also consider the more restrictive notion of a strong nonuniform exponential trichotomy and again we give a characterization in terms of admissibility properties. We emphasize that both notions are ubiquitous in the context of ergodic theory. As a nontrivial application, we show in a simple manner that the two notions of trichotomy persist under sufficiently small linear perturbations. Finally, we obtain a corresponding characterization of nonuniformly partially hyperbolic sets.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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