Area preserving analytic flows with dense orbits

The aim of this paper is to give sufficient conditions on area-preserving flows that guarantee the existence of dense orbits. We also answer a question by M.D. Hirsch [M.D. Hirsch, Dense recurrence in area-preserving flows on surfaces, Nonlinearity 12 (1999) 1545–1553]. The results of this work are a generalization of the ones in [M.D. Hirsch, Dense recurrence in area-preserving flows on surfaces, Nonlinearity 12 (1999) 1545–1553] and [H. Marzougui, Area preserving flows with a dense orbit, Nonlinearity 15 (2002) 1379– 1384].The first author was supported by MERST(Ministery of Higher Education,Scientifc Research and Technology,Tunisia)under the Spanish-Tunisian project,grant A/8322/07.The second one was partially supported by MEC(Ministerio de Educación y Ciencia,Spain)and FEDER(Fondo Europeo de Desarrollo Regional),grant MTM2005- 03868,and Fundación Séneca(Comunidad Autónoma de la Región de Murcia,Spain),grant 00684/PI/04