Random dynamics on real and complex projective surfaces
Algebraic Geometry
2022-11-08 v3 Dynamical Systems
Abstract
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that, in a number of cases, such stationary measures are invariant, and provide criteria for uniqueness, smoothness and rigidity of invariant probability measures. This involves a variety of tools from complex and algebraic geometry, random products of matrices, non-uniform hyperbolicity, as well as recent results of Brown and Rodriguez Hertz on random iteration of surface diffeomorphisms.
Cite
@article{arxiv.2006.04394,
title = {Random dynamics on real and complex projective surfaces},
author = {Serge Cantat and Romain Dujardin},
journal= {arXiv preprint arXiv:2006.04394},
year = {2022}
}