PAN, Huiping; SU, Weixu; NGUYEN, Duc-Manh

doi:10.1007/s00208-019-01897-2

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

PAN, Huiping

SU, Weixu
Fudan University [Shanghai]

NGUYEN, Duc-Manh
Institut de Mathématiques de Bordeaux [IMB]

Langue

Article de revue

Ce document a été publié dans

Mathematische Annalen. 2020

Springer Verlag

Résumé en anglais

We show that on any translation surface, if a regular point is contained in a simple closed geodesic, then it is contained in infinitely many simple closed geodesics, whose directions are dense in the unit circle. Moreover, the set of points that are not contained in any simple closed geodesic is finite. We also construct explicit examples showing that such points exist. For a surface in any hyperelliptic component, we show that this finite exceptional set is actually empty. The proofs of our results use Apisa's classifications of periodic points and of $\mathrm{GL}(2,\mathbb{R})$ orbit closures in hyperelliptic components, as well as a recent result of Eskin-Filip-Wright.< Réduire

Métadonnées

Partager cette publication !

Licence d’utilisation du document

Existence of closed geodesics through a regular point on translation surfaces

Langue

Ce document a été publié dans

Résumé en anglais

URI

DOI

Origine

Unités de recherche