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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