Random dynamics on real and complex projective surfaces-Reference-Cited by-同舟云学术

Random dynamics on real and complex projective surfaces

Published:2023-08-10 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Cantat Serge¹,Dujardin Romain²^ORCID

Affiliation:

1. IRMAR , Campus de Beaulieu, Bâtiments 22-23 263 Avenue du Général Leclerc, CS 74205, 35042 Rennes Cédex , France

2. CNRS , Laboratoire de Probabilités, Statistique et Modélisation (LPSM) , Sorbonne Université , 75005 Paris , France

Abstract

Abstract We initiate the study of random iteration of automorphisms of real and complex projective surfaces, as well as compact Kähler surfaces, focusing on the 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.

Funder

H2020 European Research Council

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2023-0038/pdf

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