Existence of orbits with non-zero torsion for certain types of surface diffeomorphisms

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概要

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• The present paper concerns the dynamics of surface diffeomorphisms. Given a diffeomorphism f of a surface S, the torsion of the orbit of a point z ∈ S is, roughly speaking, the average speed of rotation of the tangent vectors under the action of the derivative of f, along the orbit of z under f. The purpose of the paper is to identify some situations where there exist measures and orbits with non-zero torsion. We prove that every area preserving diffeomorphism of the disc which coincides with the identity near the boundary has an orbit with non-zero torsion. We also prove that a diffeomorphism of the torus ${\mathbb T}^2$, isotopic to the identity, whose rotation set has non-empty interior, has an orbit with non-zero torsion.

著者

• Boubaker Zouhour

  Universit du 7 Novembre à Carthage, Faculté des Sciences de Bizerte, Département de Mathématiques

• BEGUIN Francois

  Laboratoire dAnalyse, Géométrie et Applications, Université Paris Nord

関連論文

• Existence of orbits with non-zero torsion for certain types of surface diffeomorphisms

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