Portal de Periódicos da CAPES

Artigo Acesso aberto Produção Nacional Revisado por pares

BIBTEX RIS

The gluing orbit property, uniform hyperbolicity and large deviations principles for semiflows

2019; Elsevier BV; Volume: 267; Issue: 1 Linguagem: Inglês

10.1016/j.jde.2019.01.010

1090-2732

Thiago Bomfim, Paulo Varandas,

Advanced Differential Equations and Dynamical Systems

We introduce a gluing orbit property, weaker than specification, for both continuous maps and flows. We prove that flows with the C1-robust gluing orbit property are uniformly hyperbolic and that every uniformly hyperbolic flow satisfies the gluing orbit property. We also prove a level-1 large deviations principle and a level-2 large deviations lower bound for semiflows with the gluing orbit property. As a consequence we establish a level-1 large deviations principle for hyperbolic flows and every continuous observable, and also a level-2 large deviations lower bound. Finally, since many non-uniformly hyperbolic flows can be modeled as suspension flows we also provide criteria for such flows to satisfy uniform and non-uniform versions of the gluing orbit property.