A topological characterization of ω-limit sets for continuous flows on the projective plane
Víctor Jiménez López Gabriel Soler López
Conference Publications 2001, 2001(Special): 254-258 doi: 10.3934/proc.2001.2001.254
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Accumulation points of flows on the Klein bottle
Gabriel Soler López
Discrete & Continuous Dynamical Systems - A 2003, 9(2): 497-503 doi: 10.3934/dcds.2003.9.497
The aim of this paper is to give a topological characterization of the sets that can be $\omega$-limit of continuous dynamical systems in the Klein bottle. This problem has been recently solved for the case of the projective plane answering a problem proposed by Anosov.
keywords: Flow critical point recurrent point $\omega$-limit set. orbit regular orbit
Existence of minimal flows on nonorientable surfaces
José Ginés Espín Buendía Daniel Peralta-salas Gabriel Soler López
Discrete & Continuous Dynamical Systems - A 2017, 37(8): 4191-4211 doi: 10.3934/dcds.2017178

Surfaces admitting flows all whose orbits are dense are called minimal. Minimal orientable surfaces were characterized by J.C. Benière in 1998, leaving open the nonorientable case. This paper fills this gap providing a characterization of minimal nonorientable surfaces of finite genus. We also construct an example of a minimal nonorientable surface with infinite genus and conjecture that any nonorientable surface without combinatorial boundary is minimal.

keywords: Flow surface minimality transitivity interval and circle exchange transformations suspension

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