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.
This publication is cited in the following 7 articles:
Nagar A., Singh P., “Finiteness in Polygonal Billiards on Hyperbolic Plane”, Topol. Methods Nonlinear Anal., 58:2 (2021), 481–520
Krzysztof Frączek, Corinna Ulcigrai, “Non-ergodic $\mathbb{Z}$ -periodic billiards and infinite translation surfaces”, Invent. math., 197:2 (2014), 241
Krzysztof Frączek, Corinna Ulcigrai, “Ergodic Directions for Billiards in a Strip with Periodically Located Obstacles”, Commun. Math. Phys., 327:2 (2014), 643
Eugene Gutkin, “Billiard dynamics: An updated survey with the emphasis on open problems”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 22:2 (2012)
JEAN-PIERRE CONZE, EUGENE GUTKIN, “On recurrence and ergodicity for geodesic flows on non-compact periodic polygonal surfaces”, Ergod. Th. Dynam. Sys., 32:2 (2012), 491
Krzysztof Frączek, Corinna Ulcigrai, “Ergodic properties of infinite extensions of area-preserving flows”, Math. Ann., 354:4 (2012), 1289
Eugene Gutkin, “Capillary Floating and the Billiard Ball Problem”, J. Math. Fluid Mech., 14:2 (2012), 363
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