Escape rates for Gibbs measures

By Andrew Ferguson, Mark Pollicott. Ergodic Theory and Dynamical Systems, 2010

84 citations recorded by the source corpus.

Abstract In this paper we study the asymptotic behaviour of the escape rate of a Gibbs measure supported on a conformal repeller through a small hole. There are additional applications to the convergence of the Hausdorff dimension of the survivor set.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f82525a25c8cca22a0485e083dc2dac7c03dd908

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In Mathematical Physics

1. Mike Todd
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In Statistics and Probability

1. Mike Todd
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Citations in the corpus

• The Compound Poisson Limit Ruling Periodic Extreme Behaviour of Non-Uniformly Hyperbolic Dynamics (2012, methodology): “ample it applies to topologically transitive uniformly expanding maps of the interval with an absolutely continuous invariant probability measure (acip), including the systems studied in [BSTV03] and [FP11]. The final part of this paper is concerned with applying the above theory to non-uniformly hyp”
• Leaking chaotic systems (2012, background): “…argument has been rigorously extended for different classes of strongly chaotic systems, such as 1D expanding linear maps (Afraimovich and Bunimovich, 2010; Bakhtin and Bunimovich, 2011; Bunimovich, 2012; Bunimovich and Yurchenko, 2011; Ferguson and Pollicott, 2012; Keller and Liverani, 2009).”