Regularized variational principles for the perturbed Kepler problem

2020/03/20 by Barutello, Vivina, Ortega, Rafael, Verzini, Gianmaria · 3 citations
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.09383

Abstract

The goal of the paper is to develop a method that will combine the use of variational techniques with regularization methods in order to study existence and multiplicity results for the periodic and the Dirichlet problem associated to the perturbed Kepler system x = -(x)/(|x|³) + p(t), x ∈ ℝ^d, where d≥ 1, and p:ℝ→ℝ^d is smooth and T-periodic, T>0. The existence of critical points for the action functional associated to the problem is proved via a non-local change of variables inspired by Levi-Civita and Kustaanheimo-Stiefel techniques. As an application we will prove that the perturbed Kepler problem has infinitely many generalized T-periodic solutions for d=2 and d=3, without any symmetry assumptions on p.

Cited by

• Loop space blow-up and scale calculus
• Spatial Stark-Zeeman Systems and Their Regularizations
• A variational approach to time-dependent planar two-center Stark-Zeeman systems

Related

• Periodic solutions to relativistic Kepler problems: a variational approach
• Nearly-circular periodic solutions of perturbed relativistic Kepler problems: the fixed-period and the fixed-energy problems
• Periodic solutions to a perturbed relativistic Kepler problem
• Generalized Periodic Orbits of Time-Periodically Forced Kepler Problem Accumulating the Center and of Circular and Elliptic Restricted Three-Body Problems
• Regularization of the Kepler problem on the Sphere