Empty interior recurrence for continuous flows on surfaces
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We thank the referee for his/her useful comments on this work which helped us to improve it. This work has been partially supported by Dirección General de Investigación (Subdirección General de Proyectos de Investigación), MICINN, grants BFM2002-03512, MTM2005-03868 and MTM2008- 03679/MTM, and Fundación Séneca (Comunidad Autónoma de la Región de Murcia, Spain), grants PI-8/00807/FS/01, 00684/PI/04 and 08667/PI/08.Fecha de publicación
2009-11-16Palabras clave
FlujosConjunto ω-limite
Familia factible
Conjunto excepcional
Conjunto ω-limite excepcional
Flow
ω-limit set
Feasible family
Exceptional set
Exceptional ω-limit set
Resumen
In this paper we characterize topologically the empty interior subsets of a compact surface
S which can be ω-limit sets of recurrent orbits (but of no nonrecurrent ones) of continuous
flows on S. This culminates the classification of ω-limit sets for surface flows initiated in
[Jiménez & Soler, 2001], [Soler, 2003], [Jiménez & Soler, 2004], and [Jiménez & Soler, 2004b].
We also show that this type of ω-limit sets can always be realized (up to topological equivalence)
by smooth flows but cannot be realized by analytic flows.
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