Bifurcation of quasi-periodic solutions from equilibrium points of reversible dynamical systems
The author considers reversible analytic systems in \({\mathbb{R}}^ q\) which depend on a p-dimensional parameter y, \(\dot x=X(y,x)\), where the origin \(x=0\) is an equilibrium point for every value of y. The goal of the paper is to construct quasi-periodic solutions near the origin under some nondegeneracy conditions along the lines of KAM-theory. The main point is that multiple hyperbolic eigenvalues are admitted what was not the case in Moser's original approach. But it must be said that Moser himself formulated the generalized version of his theory in terms of Lie algebras after the Moser-Graff-tori, the first example with multiple hyperbolic eigenvalues, is constructed.
scientific article; zbMATH DE number 4050055
scientific article