Existence and Stability of Periodic Orbits for a Hamiltonian System with Homogeneous Potential of Degree Five

被引：2

作者：

Uribe, Marco ^{[1
]}

Quispe, Margarita ^{[1
]}

机构：

[1] Univ Catolica Ssma, Fac Ingn, Dept Matemat & Fis Aplicadas, Alonso Ribera 2850, Concepcion, Viii Region, Chile

来源：

DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS | 2023年 / 31卷 / 04期

关键词：

Hamiltonian systems; Periodic orbits; Stability; Averaging theory; MOTION;

D O I：

10.1007/s12591-020-00526-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the autonomous Hamiltonian system with two degrees of freedom associated to the function H = 1/2 (x(2) + y(2)) + 1/2 (p(x)(2) + p(y)(2)) + V-5(x, y), where V-5(x, y) = (A/5x(5) + Bx(3)y(2) + C/5xy(4)) which is related to a homogeneous potential of degree five. We prove the existence of different families of periodic orbits and the type of stability is analyzed through the averaging theory which guarantee the existence of such orbits on adequate sets defined by the parameters A, B, C.

引用

页码：743 / 765

页数：23

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