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Пишет друг друга пердуна (![[info]](http://lj.rossia.org/img/userinfo.gif){kind=small} oort)@ 2020-06-10 01:44:00 |
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Random dynamics on real and complex projective surfaces
Serge Cantat (IRMAR), Romain Dujardin (LPSM (UMR\_8001))
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{ä}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.
https://arxiv.org/abs/2006.04394
Serge Cantat (IRMAR), Romain Dujardin (LPSM (UMR\_8001))
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{ä}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.
https://arxiv.org/abs/2006.04394
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