Stability of the rotation set of area-preserving toral homeomorphisms
Stability of the rotation set of area-preserving toral homeomorphisms
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 …