Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces (1008.2400v1)

Abstract: We establish the background for the study of geodesics on noncompact polygonal surfaces. For illustration, we study the recurrence of geodesics on $Z$-periodic polygonal surfaces. We prove, in particular, that almost all geodesics on a topologically typical $Z$-periodic surface with boundary are recurrent.