Composition of L-S-V Maps with Random Sampling on any Bounded Interval in Parameter Space
speaker: Matteo Tanzi (King's College)abstract: Liverani-Saussol-Vaienti maps form a family of piecewise differentiable dynamical systems of the unit interval depending on one positive real parameter. The maps are everywhere expanding apart from a neutral fixed point and it is well known that, depending on the amount of expansion close to this point, they have either an absolutely continuous invariant measure and polynomial decay of correlations, or a unique physical measure that is singular and concentrated at the neutral point. I will present results on the composition of L-S-V maps whose parameters are randomly sampled so that the two contrasting behaviours are mixed. I will show that if the parameters for which there is an absolutely continuous measure are sampled with positive probability then: the stationary measure of the random system is absolutely continuous; the annealed decay rate of correlations is close (or in some cases equal) to the fastest rate of decay among those of the sampled systems; and suitably rescaled Birkhoff averages converge to limit law
timetable:
Fri 7 Jun, 11:10 - 11:55, Aula Dini
<< Go back