Monotone recurrence relations, their Birkhoff orbits and topological entropy

A generalization of the class of monotone twistmaps to maps ofs1×RNis proposed. The existence of Birkhoff orbits is studied, and a criterion for positive topological entropy is given. These results are then specialized to the case of monotone twist maps. Finally it is shown that there is a large class of symplectic maps to which the foregoing discussion applies.