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August  2017, 37(8): 4191-4211. doi: 10.3934/dcds.2017178

## Existence of minimal flows on nonorientable surfaces

 1 Departamento de Matemáticas, Universidad de Murcia (Campus de Espinardo), 30100 Espinardo-Murcia, Spain 2 Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049 Madrid, Spain 3 Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Paseo Alfonso XIII, 52, 30203 Cartagena, Spain

* Corresponding author: josegines.espin@um.es

Received  August 2016 Revised  March 2017 Published  April 2017

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.

Citation: José Ginés Espín Buendía, Daniel Peralta-salas, Gabriel Soler López. Existence of minimal flows on nonorientable surfaces. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4191-4211. doi: 10.3934/dcds.2017178
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##### References:
Construction of $M_T$ by means of a $(6, 3)$-i.e.t. with $\pi = (-3, 4, -5, 6, 1, -2)$. The circle $C$ is nonorientable. The arrows on the images of the $m_i$ mark if they are flipped by $T$
A standard saddle point (left) and a $6$-saddle point (right)
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