event
Thursday 17 Nov 2022: Random Young towers and quenched decay of correlations for randomly perturbed Lorenz systems
Andrew Larkin - Loughborough University
Harrison 103 14:30-15:30
Expanding Lorenz maps, which are obtained by taking a Poincaré section of a geometric Lorenz attractor and quotienting along stable leaves, have been studied extensively in the literature. In particular, in Díaz-Ordaz (2006), it was proved using Young towers that these map have exponential decay of correlations.
In this talk, I will consider a random dynamical system defined by taking random compositions of expanding Lorenz maps from a family where each map is 'sufficiently close' to some initial unperturbed map. I will prove that for this random system we have exponential quenched decay of correlations by using random Young towers. This involves showing that one can construct a return partition on a suitable base, where the return time function has good asymptotics, and that the random tower map satisfies the usual tower axioms. It is then a question of showing that the dynamics on the random tower can be pulled back down to the original random system.
This talk is based on my paper Quenched decay of correlations for one-dimensional random Lorenz maps (DOI:10.1007/s10883-021-09583-w).
