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. © 2014 Juliusz Schauder Centre for Nonlinear Studies.
|Journal||Topological Methods in Nonlinear Analysis|
|Publication status||Published - 1 Jan 2014|
- Lyapunov-Schmidt reduction
- Period manifold
- Periodic solution
- Small parameter
- The second order bifurcation function