Dulac’s theorem

Let x˙=f(x) be an analytic planar system, then in any bounded region of the plane there is at most a finite number of limit cyclesMathworldPlanetmath. Also any polynomial planar system has at most a finite number of limit cycles.[PL]

note about the proof: The proof was given by Dulac in 1923, but an error was found in the proof. In 1988 Jean Ecalle, Jacques Martinet, Robert Moussu, Jean Pierre Ramis and independently Yulij Ilyashenko corrected the error in the proof.[PL]


Title Dulac’s theorem
Canonical name DulacsTheorem
Date of creation 2013-03-22 14:25:21
Last modified on 2013-03-22 14:25:21
Owner Daume (40)
Last modified by Daume (40)
Numerical id 6
Author Daume (40)
Entry type Theorem
Classification msc 34C07