Topologically monotone orbits on surfaces
Abstract. The notion of Birkhoff Orbits, as shown by Aubury-Mather theory, on the annulus for twist maps has been generalized to the idea of "Monotone Orbits" for more general homeomorphisms. We further generalize this to monotone periodic orbits on other surfaces and we obtain Sharkovski type theorems using the partial order as defined by Boyland.