A topological characterization of the ω-limit sets for analytic flows on the plane, the sphere and the projective plane |
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| Authors: | Ví ctor Jimé nez Ló pez |
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| Affiliation: | a Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain
b Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain |
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| Abstract: | In this paper the ω-limit sets for analytic and polynomial differential equations on the plane are characterized up to homeomorphisms. The analogous problem is solved in full detail for analytic flows on the sphere and the projective plane. We also explain how to carry on the same program for analytic flows defined on open subsets of these surfaces. |
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| Keywords: | Analytic flow ω-limit set Projective plane Sphere Surface |
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