Stability of the rotation set of area-preserving toral homeomorphisms

Abstract

We show that if the rotation set of a homeomorphism of the torus is stable under small perturbations of the dynamics, then it is a convex polygon with rational vertices. We also show that such homeomorphisms are $C^0$-generic and have bounded rotational deviations (even for pseudo-orbits). The results hold both in the area-preserving setting and in the general setting. When the rotation set is stable, we give explicit estimates on the type of rationals that may appear as vertices of rotation sets in terms of the stability constants.

arXiv comment8 pages, 1 figure. Corrected version, to appear in Nonlinearity

References in corpus (5)

• New Rotation Sets in a Family of Torus Homeomorphisms
• A toral diffeomorphism with a non-polygonal rotation set
• Uniform bounds for diffeomorphisms of the torus and a conjecture of P. Boyland
• On annular maps of the torus and sublinear diffusion
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Cited by in corpus (2)

• On Stable and Unstable Behaviours of Certain Rotation Segments
• On the onset of diffusion in the kicked Harper model