Empty interior Recurrence for Continuous Flows on Surfaces

In this paper we characterize topologically the empty interior subsets of a compact surface S which can be -limit sets of recurrent orbits (but of no nonrecurrent ones) of continuous flows on S. This culminates the classification of -limit sets for surface flows initiated in [JS01], [Sol03], [JS04a], and [JS04b]. We also show that this type of -limit sets can always be realized (up to topological equivalence) by smooth flows but cannot be realized by analytic flows.

• Type: Journal
• Year: 2010
• Where: IJBC
• Authors: Víctor Jiménez López, Gabriel Soler López
• Keywords: -limit Sets, Continuous Flows, IJBC 2010, Smooth Flows