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


Gutkin E.
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
Gutkin E.
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

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