On a Morse conjecture for analytic flows on compact surfaces
Knowledge Area
Matemática AplicadaSponsors
The first author was supported by the research unit “Systèmes dynamiques et Combinatoire” 99UR/15-15. 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.Publication date
2009-11-15Publisher
ElsevierBibliographic Citation
MARZOUGUI, Habib, SOLER LÓPEZ, Gabriel. On a Morse conjecture for analytic flows on compact surfaces. Journal of Differential Equations 247 (10): 2681-2687, 15 November 2009. ISSN 0022-0396Keywords
Flujos de trabajo analíticoÓrbita
Transitividad topológica
Transitividad métrica
Conjetura de Morse
Límite infinito establecido
Analytic flow
Orbit
Topological transitivity
Metrical transitivity
Morse conjecture
ω-limit set
Abstract
The aim of this paper is to prove a Morse conjecture; in particular it is shown that a topologically transitive analytic flow on a compact surface is metrically transitive. We also build smooth topologically transitive flows on surfaces which are not metrically transitive.
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