return time statistics
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2011 ◽  
Vol 31 (5) ◽  
pp. 1363-1390 ◽  
Author(s):  
CHINMAYA GUPTA ◽  
MARK HOLLAND ◽  
MATTHEW NICOL

AbstractIn this paper we establish extreme value statistics for observations on a class of hyperbolic systems: planar dispersing billiard maps and flows, Lozi maps and Lorenz-like maps. In particular, we show that for time series arising from Hölder observations on these systems which are maximized at generic points the successive maxima of the time series are distributed according to the corresponding extreme value distributions for independent identically distributed processes. These results imply an exponential law for the hitting and return time statistics of these dynamical systems.



2009 ◽  
Vol 09 (01) ◽  
pp. 81-100 ◽  
Author(s):  
HENK BRUIN ◽  
MIKE TODD

We prove that multimodal maps with an absolutely continuous invariant measure have exponential return time statistics around almost every point. We also show a "polynomial Gibbs property" for these systems, and that the convergence to the entropy in the Ornstein–Weiss formula has normal fluctuations. These results are also proved for equilibrium states of some Hölder potentials.



2008 ◽  
Vol 22 (1) ◽  
pp. 18-37 ◽  
Author(s):  
Miguel Abadi ◽  
Nicolas Vergne


2003 ◽  
Vol 23 (4) ◽  
pp. 991-1013 ◽  
Author(s):  
H. BRUIN ◽  
B. SAUSSOL ◽  
S. TROUBETZKOY ◽  
S. VAIENTI


2003 ◽  
Vol 176 (1) ◽  
pp. 77-94 ◽  
Author(s):  
H. Bruin ◽  
S. Vaienti


2002 ◽  
Vol 88 (22) ◽  
Author(s):  
Nicolai Hadyn ◽  
José Luevano ◽  
Giorgio Mantica ◽  
Sandro Vaienti


1999 ◽  
Vol 131 (1-4) ◽  
pp. 68-77 ◽  
Author(s):  
Roberto Artuso


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