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Annales scientifiques de l'ENS - Parutions - série 4, 48 (2015)

Parutions < série 4, 48

ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 48, fascicule 1 (2015)

Curtis T. McMullen
Cascades in the dynamics of measured foliations
Annales scientifiques de l'ENS 48, fascicule 1 (2015), 1-39

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Résumé :
Cascades dans la dynamique des feuilletages mesurés
Nous étudions le comportement des feuilletages mesurés harmoniques sur les surfaces de Riemann compactes. Quand les périodes relatives varient, on peut observer des cascades dans la dynamique d'un tel feuilletage. Dans le cas du genre 2, on montre que le lieu de bifurcation résultant d'une telle variation est un sous-ensemble dénombrable et fermé de R, qui se plonge dans ^.

Mots-clefs : Surfaces de Riemann, différentielles abéliennes, feuilletages mesurés, périodes.

Abstract:
This paper studies the behavior of harmonic measured foliations on compact Riemann surfaces. Cascades in the dynamics of such a foliation can occur as its relative periods are varied. We show that in the case of genus 2, the bifurcation locus arising from such a variation is a closed, countable set of R that embeds in ^.

Keywords: Riemann surfaces, Abelian differentials, measured foliations, periods.

Class. math. : 30F30.


ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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