1997/04/01 by B. Coll, A. Gasull, Armengol Gasull +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Numerical methods for differential equations #Quantum chaos and dynamical systems
paper · pdf · doi:10.4153/cjm-1997-011-0
Abstract In this paper we prove, that under certain hypotheses, the planar differential equation: ˙ x = X 1 ( x , y ) + X 2 ( x , y ), ˙ y = Y 1 ( x , y ) + Y 2 ( x , y ), where ( X i , Y i ), i = 1, 2, are quasi-homogeneous vector fields, has at most two limit cycles. The main tools used in the proof are the generalized polar coordinates, introduced by Lyapunov to study the stability of degenerate critical points, and the analysis of the derivatives of the Poincar´e return map. Our results generalize those obtained for polynomial systems with homogeneous non-linearities.