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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Bomfim, Thiago¹  Varandas, Paulo¹ 

[1] Univ Fed Bahia, Dept Matemat, Av Ademar de Barros S-N, BR-40170110 Salvador, BA, Brazil

关键词: Gluing orbit property;    Specification;    Semiflows;    Hyperbolicity;    Stability;    Large deviations;   

DOI  :  10.1016/j.jde.2019.01.010

来源: Elsevier

【 摘 要 】

We introduce a gluing orbit property, weaker than specification, for both continuous maps and flows. We prove that flows with the C-1-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. (c) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free