Large deviations, gibbs measures and closed orbits for hyperbolic flows

1995 ◽  
Vol 220 (1) ◽  
pp. 219-230 ◽  
Author(s):  
Mark Pollicott
Keyword(s):  
Large Deviations ◽  
Gibbs Measures ◽  
Closed Orbits ◽  
Hyperbolic Flows

scholarly journals Multifractal analysis for weak Gibbs measures: from large deviations to irregular sets

2015 ◽  
Vol 37 (1) ◽  
pp. 79-102 ◽  
Author(s):  
THIAGO BOMFIM ◽  
PAULO VARANDAS
Keyword(s):  
Large Deviations ◽  
Gibbs Measures ◽  
Rate Function ◽  
Topological Pressure ◽  
Hölder Continuous ◽  
Continuous Potential ◽  
Hyperbolic Flows ◽  
Time Averages ◽  
Set Of Points ◽  
Level 2

In this article we prove estimates for the topological pressure of the set of points whose Birkhoff time averages are far from the space averages corresponding to the unique equilibrium state that has a weak Gibbs property. In particular, if$f$has an expanding repeller and$\unicode[STIX]{x1D719}$is a Hölder continuous potential, we prove that the topological pressure of the set of points whose accumulation values of Birkhoff averages belong to some interval$I\subset \mathbb{R}$can be expressed in terms of the topological pressure of the whole system and the large deviations rate function. As a byproduct we deduce that most irregular sets for maps with the specification property have topological pressure strictly smaller than the whole system. Some extensions to a non-uniformly hyperbolic setting, level-2 irregular sets and hyperbolic flows are also given.

scholarly journals Weak Gibbs measures and large deviations

Nonlinearity ◽  
2017 ◽  
Vol 31 (1) ◽  
pp. 49-53 ◽  
Author(s):  
C-E Pfister ◽  
W G Sullivan
Keyword(s):  
Large Deviations ◽  
Gibbs Measures

scholarly journals Sharp Large Deviations for Hyperbolic Flows

2020 ◽  
Vol 21 (12) ◽  
pp. 3791-3834
Author(s):  
Vesselin Petkov ◽  
Luchezar Stoyanov
Keyword(s):  
Large Deviations ◽  
Hyperbolic Flows ◽  
Sharp Large Deviations

Sharp large deviations for some hyperbolic flows

2012 ◽  
Vol 350 (13-14) ◽  
pp. 665-669
Author(s):  
Vesselin Petkov ◽  
Luchezar Stoyanov
Keyword(s):  
Large Deviations ◽  
Hyperbolic Flows ◽  
Sharp Large Deviations
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