Periodic solutions for nonlinear differential systems: the second- order bifurcation function. (English) Zbl 1360.34089
Summary: We are concerned here with the classical problem of Poincaré of persistence of periodic solutions under small perturbations. The main contribution of this work is to give the expression of the second-order bifurcation function in more general hypotheses than the ones already existing in the literature. We illustrate our main result constructing a second-order bifurcation function for the perturbed symmetric Euler top.
MSC:
34C25 | Periodic solutions to ordinary differential equations |
34C29 | Averaging method for ordinary differential equations |
34E10 | Perturbations, asymptotics of solutions to ordinary differential equations |
34C20 | Transformation and reduction of ordinary differential equations and systems, normal forms |
34C23 | Bifurcation theory for ordinary differential equations |