Renormalisation of correlations in a barrier billiard: Quadratic irrational trajectories

PHYSICA D-NONLINEAR PHENOMENA

卷:270

Article

Adamson, L. N. C.¹  Osbaldestin, A. H.¹ 

[1] Univ Portsmouth, Dept Math, Portsmouth PO1 3HF, Hants, England

关键词: Barrier billiards;    Renormalisation;    Quadratic irrationals;    Autocorrelation function;   

DOI  :  10.1016/j.physd.2013.12.006

来源: Elsevier

【 摘 要 】

We present an analysis of autocorrelation functions in symmetric barrier billiards using a renormalisadon approach for quadratic irrational trajectories. Depending on the nature of the barrier, this leads to either self-similar or chaotic behaviour. In the self-similar case we give an analysis of the half barrier and present a detailed calculation of the locations, asymptotic heights and signs of the main peaks in the autocorrelation function. Then we consider arbitrary barriers, illustrating that typically these give rise to chaotic correlations of the autocorrelation function which we further represent by showing the invariant sets associated with these correlations. Our main ingredient here is a functional recurrence which has been previously derived and used in work on the Harper equation, strange non-chaotic attractors and a quasi-periodically forced two-level system. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free