# Rolle’s theorem for dynamical systems in the plane

Let $\phi$ 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 $\phi$. [KGA]

## References

Title Rolle’s theorem for dynamical systems in the plane RollesTheoremForDynamicalSystemsInThePlane 2013-03-22 14:06:40 2013-03-22 14:06:40 Daume (40) Daume (40) 9 Daume (40) Theorem msc 34C08