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arXiv · 1206.0213

Existence d'un feuilletage positivement transverse à un homéomorphisme de surface

Olivier Jaulent
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Abstract

Let F be a homeomorphism of an oriented surface M that is isotopic to the identity. Le Calvez proved that if F admits a lift without fixed points to the universal covering of M, then there exists a topological foliation of M transverse to the dynamics. We generalize this result to the case where the lift of F has fixed points. We obtain a singular topological foliation whose singularities are fixed points of F. Le Calvez a montré que si F est un homéomorphisme isotope à l'identité d'une surface M admettant un relèvement au revêtement universel n'ayant pas de points fixes, alors il existe un feuilletage topologique de M transverse à la dynamique. Nous montrons que ce résultat se généralise au cas où le relèvement de F admet des points fixes. Nous obtenons alors un feuilletage topologique singulier transverse à la dynamique dont les singularités sont un ensemble fermé de points fixes de F.

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Olivier Jaulent. 2013-07-28. Existence d'un feuilletage positivement transverse à un homéomorphisme de surface. https://arxiv.org/abs/1206.0213

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