scholarly journals Extreme Value Laws for Dynamical Systems with Countable Extremal Sets

2017 ◽  
Vol 167 (5) ◽  
pp. 1244-1261 ◽  
Author(s):  
Davide Azevedo ◽  
Ana Cristina Moreira Freitas ◽  
Jorge Milhazes Freitas ◽  
Fagner B. Rodrigues
Keyword(s):  
Dynamical Systems ◽  
Extreme Value ◽  
Extremal Sets

scholarly journals Extreme value laws in dynamical systems under physical observables

2012 ◽  
Vol 241 (5) ◽  
pp. 497-513 ◽  
Author(s):  
Mark P. Holland ◽  
Renato Vitolo ◽  
Pau Rabassa ◽  
Alef E. Sterk ◽  
Henk W. Broer
Keyword(s):  
Dynamical Systems ◽  
Extreme Value

scholarly journals Extreme Value Laws in Dynamical Systems for Non-smooth Observations

2010 ◽  
Vol 142 (1) ◽  
pp. 108-126 ◽  
Author(s):  
Ana Cristina Moreira Freitas ◽  
Jorge Milhazes Freitas ◽  
Mike Todd
Keyword(s):  
Dynamical Systems ◽  
Extreme Value

Speed of convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems

2015 ◽  
Vol 15 (04) ◽  
pp. 1550028 ◽  
Author(s):  
Mark Holland ◽  
Matthew Nicol
Keyword(s):  
Dynamical Systems ◽  
Convergence Rates ◽  
Hyperbolic Systems ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Recurrence Time ◽  
Quadratic Maps ◽  
Uniformly Hyperbolic Systems ◽  
Unique Maximum

Suppose (f, 𝒳, ν) is a dynamical system and ϕ : 𝒳 → ℝ is an observation with a unique maximum at a (generic) point in 𝒳. We consider the time series of successive maxima Mn(x) := max {ϕ(x),…,ϕ ◦ fn-1(x)}. Recent works have focused on the distributional convergence of such maxima (under suitable normalization) to an extreme value distribution. In this paper, for certain dynamical systems, we establish convergence rates to the limiting distribution. In contrast to the case of i.i.d. random variables, the convergence rates depend on the rate of mixing and the recurrence time statistics. For a range of applications, including uniformly expanding maps, quadratic maps, and intermittent maps, we establish corresponding convergence rates. We also establish convergence rates for certain hyperbolic systems such as Anosov systems, and discuss convergence rates for non-uniformly hyperbolic systems, such as Hénon maps.

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