Heteroclinic orbits and rotation sets for twist maps (Q2496409)

We show how the shadowing property can be used in connection to rotation sets. We review the concept of periodic chains and the shadowing rotation property, and study a class of diffeomorphisms with invariant sets that have such property. In particular, we consider invariant sets that arise from homoclinic and heteroclinic connections for twist maps in higher dimensions. As a consequence, we can show the existence of a family of twist maps, each one with an open set of rotation vectors that are realized by points that are close to a fixed-point.