Empty interior Recurrence for Continuous Flows on Surfaces

نویسندگان

  • Víctor Jiménez López
  • Gabriel Soler López
چکیده

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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عنوان ژورنال:
  • I. J. Bifurcation and Chaos

دوره 20  شماره 

صفحات  -

تاریخ انتشار 2010