Torsion and Linking number for a surface diffeomorphism

Anna Florio (1)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon

For a C 1 diffeomorphism f : R 2 → R 2 isotopic to the identity, we prove that for any value l ∈ R of the linking number at finite time of the orbits of two points there exists at least a point whose torsion at the same finite time equals l ∈ R. As an outcome, we give a much simplier proof of a theorem by Matsumoto and Nakayama concerning torsion of measures on T 2. In addition, in the framework of twist maps, we generalize a known result concerning the linking number of periodic points: indeed, we estimate such value for any couple of points for which the limit of the linking number exists.

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]

Anna Florio. Torsion and Linking number for a surface diffeomorphism. 2018. ⟨hal-01691385v1⟩