Generic Rotation Sets in Hyperbolic Surfaces

Abstract

We show that for generic homeomorphisms homotopic to the identity in a closed and oriented surface of genus $g>1$, the rotation set is given by a union of at most $2^{5g-3}$ convex sets. Examples showing the sharpness for this asymptotic order are provided.

References in corpus (2)

• Linearisation of conservative toral homeomorphisms
• A toral diffeomorphism with a non-polygonal rotation set