The quasi-periodic centre-saddle bifurcation
Perturbations of a one-parameter family of Hamiltonian systems, \(H_{\lambda}\), are considered in the paper. It is assumed that for some value of ''bifurcation parameter'' \(\lambda_{0}\) the Hamiltonian system \(H_{\lambda_{0}}\) has lower dimensional normally parabolic invariant tori and quasi-periodic center-saddle bifurcation takes place. In the integrable case such invariant tori bifurcate into normally hyperbolic and elliptic tori. With a KAM-theoretic approach the authors prove that the whole bifurcation scenario with all lower dimensional normally parabolic tori parameterized by pertinent Cantor sets of diophantine frequency vectors persist under small non-integrable perturbations. These result are applied to perturbations of a dynamically symmetric free rigid body, namely, the Euler top.
scientific article; zbMATH DE number 1212876
scientific article