Rapid and accurate methods for computing whiskered tori and their manifolds in periodically perturbed planar circular restricted 3-body problems

DOI10.1007/S10569-021-10057-1zbMath1486.70053arXiv2105.11100OpenAlexW3172724430MaRDI QIDQ2073335

Rodney L. Anderson, Bhanu Kumar, Rafael de la Llave

Publication date: 1 February 2022

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.11100

zbMATH Keywords

three-body probleminvariant manifoldsresonanceparameterization methodwhiskered tori

Mathematics Subject Classification ID

Three-body problems (70F07) Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Celestial mechanics (70F15)

Related Items (5)

Numerical Computation of High-Order Expansions of Invariant Manifolds of High-Dimensional Tori ⋮ A simple proof of Gevrey estimates for expansions of quasi-periodic orbits: dissipative models and lower-dimensional tori ⋮ Semianalytical Computation of Heteroclinic Connections Between Center Manifolds with the Parameterization Method ⋮ Flow Map Parameterization Methods for Invariant Tori in Quasi-Periodic Hamiltonian Systems ⋮ Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem

Uses Software

• GSL

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The parameterization method for invariant manifolds. From rigorous results to effective computations
• Tools to detect structures in dynamical systems using jet transport
• Computation of whiskered invariant tori and their associated manifolds: new fast algorithms
• A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms
• Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions
• Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models
• The restricted Hill four-body problem with applications to the Earth-Moon-Sun system
• Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem
• Flow map parameterization methods for invariant tori in Hamiltonian systems
• Transition state theory with quasi-periodic forcing
• Transfers between libration-point orbits in the elliptic restricted problem
• The parameterization method for invariant manifolds. III: Overview and applications
• High-order resonant orbit manifold expansions for mission design in the planar circular restricted 3-body problem
• Arnold diffusion in the planar elliptic restricted three-body problem: mechanism and numerical verification
• Stability and Chaos in Celestial Mechanics
• Basics of regularization theory
• Dynamics and Mission Design Near Libration Points
• KAM theory without action-angle variables
• A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi‐Periodic Maps: Explorations and Mechanisms for the Breakdown of Hyperbolicity
• Invariant manifolds

This page was built for publication: Rapid and accurate methods for computing whiskered tori and their manifolds in periodically perturbed planar circular restricted 3-body problems