Rolle’s theorem for dynamical systems in the plane

Let ϕ be a smooth planar dynamical system and γ a continuousMathworldPlanetmath curve which has a tangent vector at each point (i.e. γ is differentiableMathworldPlanetmathPlanetmath). Then there is a contact point between any two points of the intersection of γ and a separating solution of ϕ. [KGA]


Title Rolle’s theorem for dynamical systemsMathworldPlanetmathPlanetmath 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