The Homoclinic Orbits in the Liénard Plane
Copyright policy )The Homoclinic Orbits in the Liénard Plane
In reply to a question, posed by Roberto Conti, concerning the stability properties of the origin to a pseudolinear system in \(\mathbb{R}^ 2\), the situation is clarified for the well-known Liénard system. The notion of the maximal elliptic sector is shown to play an important role with respect to a zero solution to be a positive global (weak) attractor. The sector consists of the origin and homoclinic orbits, whence the title.
maximal elliptic sector, attractor, homoclinic orbits, Liénard system, Applied Mathematics, Homoclinic and heteroclinic solutions to ordinary differential equations, Stability of solutions to ordinary differential equations, stability, Attractors of solutions to ordinary differential equations, Analysis, pseudolinear system
maximal elliptic sector, attractor, homoclinic orbits, Liénard system, Applied Mathematics, Homoclinic and heteroclinic solutions to ordinary differential equations, Stability of solutions to ordinary differential equations, stability, Attractors of solutions to ordinary differential equations, Analysis, pseudolinear system
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