Instability of equilibrium solutions of Hamiltonian systems with n-degrees of freedom under the existence of a single resonance and an invariant ray

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Carcamo, Daniela¹  Vidal, Claudio² 

[1] Univ Bio Bio, Dept Matemat, Fac Ciencias, Casilla 5-C,8 Reg, Concepcion, Chile

[2] Univ Bio Bio, GISDA, Fac Ciencias, Dept Matemat, Casilla 5-C,8 Reg, Concepcion, Chile

关键词: Hamiltonian system;    Equilibrium solution;    Invariant ray solution;    Lie normal form;    Single resonance;    Chetaev's Theorem;   

DOI  :  10.1016/j.jde.2018.07.022

来源: Elsevier

【 摘 要 】

In this paper we prove the instability of one equilibrium point in an autonomous Hamiltonian system with n-degrees of freedom under two assumptions: the first is the existence of a single resonance of order s (without resonance of lower order, but it could exist resonance of greater order); and the second is the existence of an invariant ray solution of the truncated Hamiltonian system up to order s. Application of our main result to the satellite problem is considered. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free