On the structure of rotation sets in hyperbolic surfaces
Alonso Juan, Brum Joaquín, Passeggi Alejandro Journal of the London Mathematical Society . 2023, 107 (4), 1173-1241; http://dx.doi.org/10.1112/jlms.12710 | Referencias: 36
AbstractSearching for a relation between the genus of a closed oriented surface and the possible geometries for homological rotation sets of its maps, we prove that this invariant for Smale diffeomorphisms is given by a union of at most convex sets, all of them containing zero. The classical theory of hyperbolic dynamics allows then to extend this bound to a ‐open and dense set of homeomorphisms, suggesting this to be a general fact. Examples showing the sharpness for this asymptotic order are provided.
