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2013
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# Eugene Gutkin

ul. Gagarina 11, 87-100 Torun, Poland
Sniadeckich 8, Warszawa 10, Poland
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, no. 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, no. 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