# American Institute of Mathematical Sciences

July  2009, 25(2): 495-509. doi: 10.3934/dcds.2009.25.495

## The Poincaré-Bendixson Theorem on the Klein bottle for continuous vector fields

 1 Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Caixa Postal 668, CEP 13560-970 São Carlos (SP), Brazil, Brazil, Brazil

Received  July 2008 Revised  January 2009 Published  June 2009

We present a version of the Poincaré-Bendixson Theorem on the Klein bottle $K^2$ for continuous vector fields. As a consequence, we obtain the fact that $K^2$ does not admit continuous vector fields having a $\omega$-recurrent injective trajectory.
Citation: D. P. Demuner, M. Federson, C. Gutierrez. The Poincaré-Bendixson Theorem on the Klein bottle for continuous vector fields. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 495-509. doi: 10.3934/dcds.2009.25.495
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