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

Fernando Alcalde  Cuesta; Françoise  Dal'Bo; Matilde  Martínez; Alberto  Verjovsky

doi:10.3934/dcds.2016001

Article Contents

2016, Volume 36, Issue 9: 4619-4635. Doi: 10.3934/dcds.2016001

This issue Previous Article Next Article Parameterization of slow-stable manifolds and their invariant vector bundles: Theory and numerical implementation

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

1.
GeoDynApp - ECSING Group
2.
Institut de Recherche Mathématiques de Rennes, Université de Rennes 1, F-35042 Rennes
3.
Instituto de Matemática y Estadística Rafael Laguardia, Facultad de Ingeniería, Universidad de la República, J. Herrera y Reissig 565, C.P. 11300 Montevideo
4.
Universidad Nacional Autónoma de México, Apartado Postal 273, Admon. de correos #3, C.P. 62251 Cuernavaca, Morelos

Received: June 2015

Revised: March 2016

Published: May 2017

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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.

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Mathematics Subject Classification: 37C85, 37D40, 57R30.

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References

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