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arXiv · 1403.7533

Uniform bounds for diffeomorphisms of the torus and a conjecture of P. Boyland

Salvador Addas-Zanata
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Abstract

We consider $C^{1+ε}$ diffeomorphisms of the torus, denoted $f,$ homotopic to the identity and whose rotation sets have interior. We give some uniform bounds on the displacement of points in the plane under iterates of a lift of $f,$ relative to vectors in the boundary of the rotation set and we use these estimates in order to prove that if such a diffeomorphism $f$ preserves area, then the rotation vector of the area measure is an interior point of the rotation set. This settles a strong version of a conjecture proposed by P. Boyland. We also present some new results on the realization of extremal points of the rotation set by compact $f$-invariant subsets of the torus.

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Salvador Addas-Zanata. 2014-04-02. Uniform bounds for diffeomorphisms of the torus and a conjecture of P. Boyland. https://doi.org/10.1112/jlms%2Fjdu081

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