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PROC

Please refer to Full Text.

keywords:

DCDS

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.

DCDS

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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