Eugene Gutkin

Address: ul. Gagarina 11, 87-100 Torun, Poland
Sniadeckich 8, Warszawa 10, Poland

E-mail: gutkin@mat.umk.pl, gutkin@impan.pl

University: Nicolaus Copernicus University
Mathematics Institute of the Polish Academy of Sciences

Publications:

Gutkin E.

Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces
2010, vol. 15, nos. 4-5, pp. 482-503

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

Citation: Gutkin E., Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces, Regular and Chaotic Dynamics, 2010, vol. 15, nos. 4-5, pp. 482-503

DOI:10.1134/S1560354710040064

Gutkin E.

Billiard dynamics: a survey with the emphasis on open problems on billiards
2003, vol. 8, no. 1, pp. 1-13

Abstract

This is a brief survey of the subject, emphasizing the open problems.

Citation: Gutkin E., Billiard dynamics: a survey with the emphasis on open problems on billiards, Regular and Chaotic Dynamics, 2003, vol. 8, no. 1, pp. 1-13

DOI:10.1070/RD2003v008n01ABEH000222

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