Isochronicity and commutation of polynomial vector fields
Copyright policy )Isochronicity and commutation of polynomial vector fields
We study a connection between the isochronicity of a center of a polynomial vector field and the existence of a polynomial commuting system. We demonstrate an isochronous system of degree 4 which does not commute with any polynomial system. We prove that among the Newton polynomial systems only the Lienard and Abel systems may commute with transversal polynomial fields. We give a full and constructive description of centralizers of the Abel polynomial systems. We give new examples of isochronous systems.
21 pages, LaTeX, 5 PostScript Figures
isochronic center, Local and nonlocal bifurcation theory for dynamical systems, Bifurcations of limit cycles and periodic orbits in dynamical systems, polynomial vector field, FOS: Mathematics, Dynamical Systems (math.DS), singular point, periodic trajectory, Sabatini conjecture, Mathematics - Dynamical Systems, 34C05
isochronic center, Local and nonlocal bifurcation theory for dynamical systems, Bifurcations of limit cycles and periodic orbits in dynamical systems, polynomial vector field, FOS: Mathematics, Dynamical Systems (math.DS), singular point, periodic trajectory, Sabatini conjecture, Mathematics - Dynamical Systems, 34C05
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