CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

18 août 2020 de 10 h 00 à 11 h 00 (heure de Montréal/HNE) Réunion Zoom

Rigorously validated estimation of statistical properties of expanding maps

Séminaire par Caroline Wormell (University of Sydney, Australia)

Full-branch uniformly expanding maps and their long-time statistical quantities serve as common models for chaotic dynamics, as well as having applications to number theory. I will present an efficient method to compute important statistical quantities such as physical invariant measures, which can obtain rigorously validated bounds. To accomplish this, a Chebyshev Galerkin discretisation of transfer operators of these maps is constructed; the spectral data at the eigenvalue 1 is then approximated from this discretisation. Using this method we obtain validated estimates of Lyapunov exponents and diffusion coefficients that are accurate to over 100 decimal places. These methods may also fruitfully be extended to non-uniformly expanding maps of Pomeau-Manneville type, which have largely been altogether resistant to numerical study.