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arXiv · 1507.03905

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

Thiago Bomfim·Paulo Varandas
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Abstract

In this article we introduce a gluing orbit property, weaker than specification, for both 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 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.

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Thiago Bomfim, Paulo Varandas. 2015-07-14. The gluing orbit property, uniform hyperbolicity and large deviations principles for semiflows. https://arxiv.org/abs/1507.03905

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