PERIODIC SOLUTIONS TO A PERTURBED RELATIVISTIC KEPLER PROBLEM

被引：11

作者：

Boscaggin, Alberto ^{[1
]}

Dambrosio, Walter ^{[1
]}

Feltrin, Guglielmo ^{[2
]}

机构：

[1] Univ Torino, Dept Math Giuseppe Peano, Via Carlo Alberto 10, I-10123 Turin, Italy

[2] Univ Udine, Dept Math Comp Sci & Phys, Via Sci 206, I-33100 Udine, Italy

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2021年 / 53卷 / 05期

关键词：

relativistic Kepler problem; periodic solutions; invariant tori; nearly integrable Hamiltonian systems; action-angle coordinates; HAMILTONIAN-SYSTEMS; PERTURBATIONS; PARTICLE; SYMMETRY; MOTIONS; FIELD;

D O I：

10.1137/20M1333547

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the perturbed relativistic Kepler problem d/dt (m((x)overdot)/root 1 - vertical bar((x)overdot)vertical bar(2)/c(2)) = -alpha x/vertical bar x vertical bar(3) + epsilon del U-x(t, x), x is an element of R-2 \ {0}, where m, alpha > 0, where c is the speed of light, and U(t, x) is a function T-periodic in the first variable. For epsilon > 0 sufficiently small, we prove the existence of T-periodic solutions with prescribed winding number, bifurcating from invariant tori of the unperturbed problem.

引用

页码：5813 / 5834

页数：22

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