Periodic Solutions and KAM Tori in a Triaxial Potential

被引：10

作者：

Palacian, J. F. ^{[1
,2
]}

Vidal, C. ^{[3
]}

Vidarte, J. ^{[4
]}

Yanguas, P. ^{[1
,2
]}

机构：

[1] Univ Publ Navarra, Dept Ingn Matemat & Informat, Pamplona 31006, Spain

[2] Univ Publ Navarra, Inst Adv Mat INAMAT, Pamplona 31006, Spain

[3] Univ Bio Bio, Fac Ciencias, Dept Matemat, GISDA, Concepcion, VIII Region, Chile

[4] Univ Bio Bio, Dept Matemat, Fac Ciencias, Concepcion, VIII Region, Chile

来源：

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2017年 / 16卷 / 01期

关键词：

resonant Hamiltonians and 1: 1: 1 resonance; galactic potentials and potentials from molecular physics; normalization and reduction; averaging; reduced space and invariants; Reeb's theorem; periodic solutions and linear stability; KAM tori; HAMILTONIAN-SYSTEMS; 1-1-1; RESONANCE; ORBITS; PERTURBATIONS; OSCILLATORS; SYMMETRY;

D O I：

10.1137/16M1082925

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The existence and stability of periodic solutions for an autonomous Hamiltonian system in 1: 1: 1 resonance depending on two real parameters a and beta is established using reduction and averaging theories. The different types of periodic solutions as well as their bifurcation curves are characterized in terms of the parameters. The linear stability of each periodic solution, together with the determination of KAM 3-tori encasing some of the linearly stable periodic solutions, is proved.

引用

页码：159 / 187

页数：29

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