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We prove the existence of an open and dense set ⊂Homeo 0 ( 2 ) (where Homeo 0 ( 2 ) denotes the set of toral homeomorphisms homotopic to the identity) such that the rotation set of any element in  is a rational polygon. We also extend this result to the set of axiom A diffeomorphisms in Homeo 0 ( 2 ). Further, we observe the existence of minimal sets whose rotation set is a non‐trivial segment, for an open set in Homeo 0 ( 2 ).

Rational polygons as rotation sets of generic homeomorphisms of the two torus