Home > Articles > Published articles > On a conjecture on the integrability of Liénard systems |
Additional title: | We prove a conjecture on the integrability of Liénard systems |
Date: | 2020 |
Abstract: | We consider the Liénard differential systems ̇x=y+F(x), ̇y=x (1), in C2 where F(x) is an analytic function satisfying F(0) = 0 and F'(0) ≠ 0. Then these systems have a strong saddle at the origin of coordinates. It has been conjecture that if such systems have an analytic first integral defined in a neighborhood of the origin, then the function F(x) is linear, i. e. F(x) = ax. Here we prove this conjecture, and show that when F(x) is linear and system (1) has an analytic first integral, this is a polynomial. |
Grants: | Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Liénard system ; First integral ; Strong saddle |
Published in: | Rendiconti del Circolo Matematico di Palermo, Vol. 69, Issue 1 (April 2020) , p. 209-216, ISSN 1973-4409 |
Postprint 10 p, 300.0 KB |