UoP maths seminar (2013-14)
Renormalisation of correlations in a barrier billiard: Quadratic irrational trajectories.
Speaker: Luke Adamson
Venue: Wednesday 5th March 2014, 2pm, LG2.04a (refreshments provided)
Abstract: We present an analysis of autocorrelation functions in symmetric barrier billiards using a renormalisation 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 which we further represent by showing the invariant sets on which they lie. Our main ingredient 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.