Open AccessOn the analytic integrability of the Liénard analytic differential systems
Author(s) -
Jaume Llibre,
Clàudìa Valls
Publication year - 2015
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2016.21.557
Subject(s) - differential (mechanical device) , analytic function , mathematics , singular point of a curve , analytic element method , pure mathematics , point (geometry) , mathematical analysis , mathematical physics , physics , geometry , thermodynamics , finite element method
Agraïments: The second author is supported by Portuguese National Funds through FCT - Fundaçâo para a Ciência e a Tecnologia trough UID/MAT/04459/20We consider the Liénard analytic differential systems x = y, y =-g(x) -f(x)y, where f,g: R R are analytic functions and the origin is an isolated singular point. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the origin and the existence of global analytic first integrals