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Pré-Publication, Document De Travail Année : 2014

Existence of torsion-low maximal identity isotopies for area preserving surface homeomorphisms

Jingzhi Yan
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Résumé

The paper concerns area preserving homeomorphisms of surfaces that are isotopic to the identity. The purpose of the paper is to find a maximal identity isotopy such that we can give a fine descriptions of the dynamics of its transverse foliation. We will define a kind of identity isotopies: torsion-low isotopies. In particular, when $f$ is a diffeomorphism with finitely many fixed points such that every fixed point is not degenerate, an identity isotopy $I$ of $f$ is torsion-low if and only if for every point $z$ fixed along the isotopy, the (real) rotation number $\rho(I,z)$, which is well defined when one blows-up $f$ at $z$, is contained in $(-1,1)$. We will prove the existence of torsion-low maximal identity isotopies, and we will deduce the local dynamics of the transverse foliations of any torsion-low maximal isotopy near any isolated singularity.
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Dates et versions

hal-01063233 , version 1 (12-09-2014)

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Jingzhi Yan. Existence of torsion-low maximal identity isotopies for area preserving surface homeomorphisms. 2014. ⟨hal-01063233⟩
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