On correlation decay in low-dimensional systems
Queen Mary University of London, School of Mathematical Sciences - Mile End Road, London E1 4NS, UK
Received: 13 August 2013
Accepted: 23 October 2013
While the decay of correlations in dynamical systems has been discussed in the physics and mathematics literature for several decades, there exists virtually no nontrivial example where the actual decay rates can be computed explicitly. We construct a class of simple dynamical systems for which all correlation properties, in particular, the entire spectrum of the Perron-Frobenius operator, are accessible by analytical means. As an application we discuss an example of an interval map with a small number of branches where the decay of correlations can be made arbitrarily fast. The example can be viewed as the simplest toy model which gives rise to a crossover from transient to asymptotic behaviour with predictable crossover time scale. The model class introduced here points towards relations between correlation decay and Lyapunov spectra.
PACS: 05.45.Ac – Low-dimensional chaos / 02.30.Tb – Operator theory
© EPLA, 2013