Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems
Copyright policy )Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems
In this paper we completely characterize trivial isochronous centers of degrees 5 and 7. Precisely, we provide formulas, up to linear change of coordinates, for the Hamiltonian H of the isochronous centers such that H =(f_1^2 f_2^2)/2 has degrees 6 and 8, and f = (f_1, f_2): R^2 R^2 is a polynomial map with D f = 1 and f(0,0) = (0,0).
isochronous centers, Jacobian conjecture, Isochronous centers, Polynomial Hamiltonian systems, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, polynomial Hamiltonian systems, Periodic solutions to ordinary differential equations, Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
isochronous centers, Jacobian conjecture, Isochronous centers, Polynomial Hamiltonian systems, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, polynomial Hamiltonian systems, Periodic solutions to ordinary differential equations, Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
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