Geodesic
Cascades in the dynamics of measured foliations
[Cascades dans la dynamique des feuilletages mesurés]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 48 (2015) no. 1, pp. 1-39.

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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 ωω.

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 ωω.

Publié le :
DOI : 10.24033/asens.2237
Classification : 30F30.
Keywords: Riemann surfaces, Abelian differentials, measured foliations, periods.
Mots-clés : Surfaces de Riemann, différentielles abéliennes, feuilletages mesurés, périodes. 
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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://geodesic.mathdoc.fr/articles/10.24033/asens.2237/

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