scholarly journals Sharp Error Terms for Return Time Statistics under Mixing Conditions

2008 ◽  
Vol 22 (1) ◽  
pp. 18-37 ◽  
Author(s):  
Miguel Abadi ◽  
Nicolas Vergne
Keyword(s):  
Return Time ◽  
Mixing Conditions ◽  
Error Terms ◽  
Return Time Statistics ◽  
Sharp Error

scholarly journals RETURN TIME STATISTICS OF INVARIANT MEASURES FOR INTERVAL MAPS WITH POSITIVE LYAPUNOV EXPONENT

2009 ◽  
Vol 09 (01) ◽  
pp. 81-100 ◽  
Author(s):  
HENK BRUIN ◽  
MIKE TODD
Keyword(s):  
Lyapunov Exponent ◽  
Invariant Measures ◽  
Return Time ◽  
Continuous Invariant Measure ◽  
Absolutely Continuous ◽  
Interval Maps ◽  
Absolutely Continuous Invariant Measure ◽  
Normal Fluctuations ◽  
Return Time Statistics ◽  
Absolutely Continuous Invariant

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.

scholarly journals Return time statistics via inducing

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

Correlation decay and return time statistics

1999 ◽  
Vol 131 (1-4) ◽  
pp. 68-77 ◽  
Author(s):  
Roberto Artuso
Keyword(s):  
Return Time ◽  
Correlation Decay ◽  
Return Time Statistics

scholarly journals Extreme value theory and return time statistics for dispersing billiard maps and flows, Lozi maps and Lorenz-like maps

2011 ◽  
Vol 31 (5) ◽  
pp. 1363-1390 ◽  
Author(s):  
CHINMAYA GUPTA ◽  
MARK HOLLAND ◽  
MATTHEW NICOL
Keyword(s):  
Time Series ◽  
Hyperbolic Systems ◽  
Return Time ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Distributed Processes ◽  
Return Time Statistics ◽  
Generic Points ◽  
Lozi Maps

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.

scholarly journals Return time statistics for unimodal maps

2003 ◽  
Vol 176 (1) ◽  
pp. 77-94 ◽  
Author(s):  
H. Bruin ◽  
S. Vaienti
Keyword(s):  
Return Time ◽  
Unimodal Maps ◽  
Return Time Statistics

scholarly journals Multifractal Properties of Return Time Statistics

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

scholarly journals Sharp Error Term in Local Limit Theorems and Mixing for Lorentz Gases with Infinite Horizon

2021 ◽  
Vol 382 (3) ◽  
pp. 1625-1689
Author(s):  
Françoise Pène ◽  
Dalia Terhesiu
Keyword(s):  
Local Limit Theorem ◽  
Infinite Horizon ◽  
Local Limit ◽  
Return Time ◽  
Tail Probability ◽  
Higher Order ◽  
Error Rates ◽  
Sinai Billiard ◽  
Discrete Time Case ◽  
Sharp Error

AbstractWe obtain sharp error rates in the local limit theorem for the Sinai billiard map (one and two dimensional) with infinite horizon. This result allows us to further obtain higher order terms and thus, sharp mixing rates in the speed of mixing of dynamically Hölder observables for the planar and tubular infinite horizon Lorentz gases in the map (discrete time) case. We also obtain an asymptotic estimate for the tail probability of the first return time to the initial cell. In the process, we study families of transfer operators for infinite horizon Sinai billiards perturbed with the free flight function and obtain higher order expansions for the associated families of eigenvalues and eigenprojectors.

Sign in / Sign up

Export Citation Format

Share Document