Sur la dynamique des diff\'eomorphismes birationnels des surfaces alg\'ebriques r\'eelles : ensemble de Fatou et lieu r\'eel

TL;DR

This paper explores the dynamics of birational diffeomorphisms on real algebraic surfaces, providing examples and analyzing conditions under which simple real dynamics coexist with complex dynamics, highlighting their exceptional nature.

Contribution

It presents an example of such a transformation on P^1xP^1 and establishes that this scenario is exceptional, imposing strong topological and dynamical constraints.

Findings

Example of a birational diffeomorphism on P^1xP^1 with simple real dynamics

Such configurations are rare and imply significant topological restrictions

Strong conditions relate real topology to complex dynamics

Abstract

This text deals with birationnal diffeomorphisms of real algebraic surfaces which have simple real dynamics and rich complex dynamics. We give an example of such a transformation on P^1xP^1, then we show that this situation is exceptional and implies strong conditions on both the topology of the real locus and the real dynamics.