English

Existence of minimal flows on nonorientable surfaces

Dynamical Systems 2017-01-18 v2

Abstract

Surfaces admitting flows all whose orbits are dense are called minimal. Minimal orientable surfaces were characterized by J.C. Beni\`{e}re 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

Cite

@article{arxiv.1608.08788,
  title  = {Existence of minimal flows on nonorientable surfaces},
  author = {J. G. Espín Buendía and D. Peralta-Salas and G. Soler López},
  journal= {arXiv preprint arXiv:1608.08788},
  year   = {2017}
}

Comments

20 pages

R2 v1 2026-06-22T15:36:20.523Z