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Dynamique des applications rationnelles

Abstract : This thesis is devoted to the dynamical study of rational maps in projective spaces. It is divided into five chapters. The first one presents the analytic and formal classification of a special class of superattracting germs. In the second chapter, it is proved that the Green current of an arbitrary rational map has strong singularities only on the indeterminacy set of the map. In the third chapter, the case of applications on multi-projective surfaces is treated in detail. The fourth chapter contains an optimal convergence theorem for curves towards the Green current in the case of birational maps of surfaces. Finally the last chapter is devoted to the study of some examples.
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Contributor : Charles Favre <>
Submitted on : Wednesday, October 15, 2003 - 10:56:35 AM
Last modification on : Tuesday, May 7, 2019 - 6:30:09 PM
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  • HAL Id : tel-00003577, version 1


Charles Favre. Dynamique des applications rationnelles. Mathématiques [math]. Université Paris Sud - Paris XI, 2000. Français. ⟨tel-00003577⟩



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