# Rolle’s theorem for dynamical systems in the plane

Let $\varphi $ be a smooth planar dynamical system and $\gamma $ a continuous^{} curve which has a tangent vector at each point (i.e. $\gamma $ is differentiable^{}). Then there is a contact point between any two points of the intersection of $\gamma $ and a separating solution of $\varphi $.
[KGA]

## References

- KGA Khovanskiĭ, A.G.: Fewnomials. American Mathematical Society, Providence, 1991.

Title | Rolle’s theorem for dynamical systems^{} in the plane |
---|---|

Canonical name | RollesTheoremForDynamicalSystemsInThePlane |

Date of creation | 2013-03-22 14:06:40 |

Last modified on | 2013-03-22 14:06:40 |

Owner | Daume (40) |

Last modified by | Daume (40) |

Numerical id | 9 |

Author | Daume (40) |

Entry type | Theorem |

Classification | msc 34C08 |