Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology

Pages: 4619 - 4635, Volume 36, Issue 9, September 2016      doi:10.3934/dcds.2016001

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Fernando Alcalde Cuesta - GeoDynApp - ECSING Group, Spain (email)
Françoise Dal'Bo - Institut de Recherche Mathématiques de Rennes, Université de Rennes 1, F-35042 Rennes, France (email)
Matilde Martínez - Instituto de Matemática y Estadística Rafael Laguardia, Facultad de Ingeniería, Universidad de la República, J. Herrera y Reissig 565, C.P. 11300 Montevideo, Uruguay (email)
Alberto Verjovsky - Universidad Nacional Autónoma de México, Apartado Postal 273, Admon. de correos #3, C.P. 62251 Cuernavaca, Morelos, Mexico (email)

Abstract: We consider a minimal compact lamination by hyperbolic surfaces. We prove that if no leaf is simply connected, then the horocycle flow on its unitary tangent bundle is minimal.

Keywords:  Hyperbolic surfaces, geometrically infinite surfaces, horocycle flows, hyperbolic laminations, minimality.
Mathematics Subject Classification:  37C85, 37D40, 57R30.

Received: June 2015;      Revised: March 2016;      Available Online: May 2016.