Center problem for trigonometric Liénard systems
MetadataShow full item record
We give a complete algebraic characterization of the non-degenerated centers for planar trigonometric Liénard systems. The main tools used in our proof are the classical results of Cherkas on planar analytic Liénard systems and the characterization of some subfields of the quotient field of the ring of trigonometric polynomials. Our results are also applied to some particular subfamilies of planar trigonometric Liénard systems. The results obtained are reminiscent of the ones for planar polynomial Liénard systems but the proofs are different.
Is part ofJournal of Differential Equations, 2017, vol. 263, p. 3928-3942
European research projects
The following license files are associated with this item:
Showing items related by title, author, creator and subject.
Gasull i Embid, Armengol; Giné, Jaume (Springer International Publishing, 2017)We characterize the local analytic integrability of weak saddles for complex Lienard systems, x˙ = y−F(x), y˙ = ax, 0 = a ∈ C, with F analytic at 0 and F(0) = F (0) = 0. We prove that they are locally integrable at the ...
Gasull, Armengol; Giné, Jaume; Valls, Claudia (Springer, 2020)Given a planar analytic differential equation with a critical point which is a weak focus of order k, it is well known that at most k limit cycles can bifurcate from it. Moreover, in case of analytic Liénard differential ...
Giné, Jaume; Valls, Claudia (Elsevier, 2017)In this paper we study the center problem for Abel polynomial differential equations of second kind. Computing the focal values and using modular arithmetics and Gröbner bases we find the center conditions for such systems ...