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

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

2010-08-13

arxiv.org/abs/1008.2400v1

Regular and Chaotic Dynamics, 2010, Vol. 15, Nos. 4-5, pp. 482-503

Mathematics

Dynamical Systems

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

Scientific paper

10.1134/S1560354710040064

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.

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