Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces

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.

34 pages, 13 figures. To be published in V. V. Kozlov's Festschrift

References in corpus (1)

• Generalized staircases: recurrence and symmetry

Cited by in corpus (5)

• Capillary floating and the billiard ball problem
• On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces
• Ergodic directions for billiards in a strip with periodically located obstacles
• Billiard Dynamics: An Updated Survey with the Emphasis on Open Problems
• Ergodic properties of infinite extensions of area-preserving flows