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 & Continuous Dynamical Systems - A, 2009, 25 (2) : 495-509. doi: 10.3934/dcds.2009.25.495
[1]

Peng Luo. Comparison theorem for diagonally quadratic BSDEs. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020374

[2]

Yifan Chen, Thomas Y. Hou. Function approximation via the subsampled Poincaré inequality. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 169-199. doi: 10.3934/dcds.2020296

[3]

Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Klein-gordon equation. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020448

[4]

Yuri Fedorov, Božidar Jovanović. Continuous and discrete Neumann systems on Stiefel varieties as matrix generalizations of the Jacobi–Mumford systems. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020375

[5]

Mingjun Zhou, Jingxue Yin. Continuous subsonic-sonic flows in a two-dimensional semi-infinitely long nozzle. Electronic Research Archive, , () : -. doi: 10.3934/era.2020122

2019 Impact Factor: 1.338

Metrics

  • PDF downloads (44)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]