I wanna know is my understanding on PB theorem correct or not. What I understand is, if I define a differentiable real dynamical system on an open subset of plane(so the theorem only applies to dynamical systems in 2 spatial dimensions), the system, as [itex] t\to \infty [/itex], will have only one of the following behaviours:(adsbygoogle = window.adsbygoogle || []).push({});

1) Stands still at a point.

2) Moves periodically.

3) Moves from one equilibrium point to another with no periodicity.

Thanks

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Clarification of Poincaré–Bendixson theorem!

Loading...

Similar Threads - Clarification Poincaré–Bendixson theorem | Date |
---|---|

B Gram-Schmidt Orthonormalization ... Garling Theorem 11.4.1 . | Mar 10, 2018 |

Clarification: proof that perfect subsets of R^k uncountable | Feb 12, 2016 |

Clarification about Poincaré's conjecture | Feb 28, 2015 |

Cylinder sets, some clarification | Feb 24, 2015 |

Proof about a limit property clarification | Jun 3, 2013 |

**Physics Forums - The Fusion of Science and Community**