Cascades in the dynamics  of measured foliations

McMullen, Curtis T.

doi:10.24033/asens.2237

Cascades in the dynamics of measured foliations
[Cascades dans la dynamique des feuilletages mesurés]

McMullen, Curtis T.

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 48 (2015) no. 1, pp. 1-39.

Résumé
Abstract

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 $ω^{ω}$ .

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 $ω^{ω}$ .

Publié le : 2015-09-24

DOI : 10.24033/asens.2237

Classification : 30F30.
Keywords: Riemann surfaces, Abelian differentials, measured foliations, periods.
Mot clés : Surfaces de Riemann, différentielles abéliennes, feuilletages mesurés, périodes.

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     title = {Cascades in the dynamics  of measured foliations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1--39},
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McMullen, Curtis T. Cascades in the dynamics  of measured foliations. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 48 (2015) no. 1, pp. 1-39. doi : 10.24033/asens.2237. http://www.numdam.org/articles/10.24033/asens.2237/

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