English

Torsion and Linking number for a surface diffeomorphism

Dynamical Systems 2018-11-16 v3

Abstract

For a C1\mathcal{C}^1 diffeomorphism f:R2R2f:\mathbb{R}^2\rightarrow\mathbb{R}^2 isotopic to the identity, we prove that for any value lRl\in\mathbb{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 lRl\in\mathbb{R}. As an outcome, we give a much simpler proof of a theorem by Matsumoto and Nakayama concerning torsion of measure on T2\mathbb{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.

Keywords

Cite

@article{arxiv.1801.07751,
  title  = {Torsion and Linking number for a surface diffeomorphism},
  author = {Anna Florio},
  journal= {arXiv preprint arXiv:1801.07751},
  year   = {2018}
}
R2 v1 2026-06-22T23:53:35.302Z