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]

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