This article is cited in 7 papers

On the 60th birthday of professor V.V. Kozlov

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

Eugene Gutkin<sup>ab

a</sup> Nicolaus Copernicus University (UMK), Chopina 12/18, Torun 87-100
^b Mathematics Institute of the Polish Academy of Sciences (IMPAN), Sniadeckich 8, Warszawa 10, Poland

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

Keywords: (periodic) polygonal surface, geodesic, skew product, cross-section, displacement function, recurrence, transience, ergodicity.

MSC: 37C40, 37D50, 37E35

Received: 12.03.2010
Accepted: 25.03.2010

Language: English

DOI: 10.1134/S1560354710040064

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