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January, 2013 Existence of orbits with non-zero torsion for certain types of surface diffeomorphisms
François BÉGUIN, Zouhour Rezig BOUBAKER
J. Math. Soc. Japan 65(1): 137-168 (January, 2013). DOI: 10.2969/jmsj/06510137


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 $z\in S$ 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.


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François BÉGUIN. Zouhour Rezig BOUBAKER. "Existence of orbits with non-zero torsion for certain types of surface diffeomorphisms." J. Math. Soc. Japan 65 (1) 137 - 168, January, 2013.


Published: January, 2013
First available in Project Euclid: 24 January 2013

zbMATH: 1268.37064
MathSciNet: MR3034401
Digital Object Identifier: 10.2969/jmsj/06510137

Primary: 37E30 , 37E45

Keywords: rotation sets , Ruelle number , surface diffeomorphisms , torsion

Rights: Copyright © 2013 Mathematical Society of Japan


Vol.65 • No. 1 • January, 2013
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