Sur le groupe de Cremona : aspects algébriques et
dynamiques

Abstract : In this thesis we prove that an automorphism of the group of polynomial automorphisms of the affine plane is the composition of an interior automorphism and an automorphism of the field of complex numbers; we generalize this result for the Cremona group. In the first case the proof is based on the amalgated structure of the group; in the second case the proof is based on a classification of maximal abelian subgroups. Then we are interested in representations of some lattices of Lie groups in the Cremona group. We obtain in particular the "rigidity" of SL(3,Z) and that there is no embedding from some lattices in the Cremona group. Finally we give a curious family of birational transformations:although they have some caracteristics of transformations without dynamic, numerical experiments reveal some chaotic orbits in the complement of two zones where the adherence of the orbits are a torus or a circle.
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Theses
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https://tel.archives-ouvertes.fr/tel-00125492
Contributor : Julie Deserti <>
Submitted on : Friday, January 19, 2007 - 7:45:15 PM
Last modification on : Friday, November 16, 2018 - 1:23:10 AM
Long-term archiving on : Tuesday, April 6, 2010 - 8:11:29 PM

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  • HAL Id : tel-00125492, version 1

Citation

Julie Déserti. Sur le groupe de Cremona : aspects algébriques et
dynamiques. Mathématiques [math]. Université Rennes 1, 2006. Français. ⟨tel-00125492⟩

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