Degenerate bifurcation points of periodic solutions of autonomous Hamiltonian systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:202

Article

Radzki, W ; Rybicki, S

关键词: Hamiltonian system;    periodic solution;    bifurcation;    emanation;    branching point;    bifurcation index;    topological degree for SO(2)-equivariant gradient maps;   

DOI  :  10.1016/j.jde.2004.03.037

来源: Elsevier

【 摘 要 】

We study connected branches of nonconstant 2pi-periodic solutions of the Hamilton equation. x(overdot)(t) = lambdaVdelH(x(t)), where lambdaepsilon(0,+infinity), H epsilon C-2(R-n x R-n, R) and del(2)H(x(0)) = [(A)(0) (0)(B)] for x(0) epsilon delH(-1)(0). The Hessian del(2) H(x(0)) can be singular. We formulate sufficient conditions for the existence of such branches bifurcating from given (x(0), lambda(0)). As a consequence we prove theorems concerning the existence of connected branches of arbitrary periodic nonstationary trajectories of the Hamiltonian system x(overdot)(t) = JdelH(x(t)) emanating from x(0). We describe also minimal periods of trajectories near x(0). (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free