The goal of this paper is to provide a methodology to prove existence of (fiberwise hyperbolic) real-analytic invariant tori in real-analytic quasi-periodic skew-product dynamical systems that present nearly-invariant tori of the same characteristics. The methodology is based on the application of a Newton-Kantorovich theorem whose hypotheses are tested using Fourier analysis methods for a numerical approximation of the parameterization of an invariant torus.
Rapid GPU-Assisted Search and Parameterization-Based Refinement and Continuation of Connections between Tori in Periodically Perturbed Planar Circular Restricted 3-Body Problems
Numerical computation of high-order expansions of invariant manifolds of high-dimensional tori
Universitat de Barcelona（巴塞罗那大学）；Barcelona Expert Center (BEC)（巴塞罗那卓越中心）；Institute of Marine Sciences (ICM)（海洋科学研究所）；Consejo Superior de Investigaciones Científicas (CSIC)（西班牙国家研究委员会）
On the existence of full dimensional KAM tori for 1D periodic nonlinear Schrödinger equation
School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院）；Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology（华中科技大学工程建模与科学计算湖北省重点实验室）
Parallelized computation of quasi-periodic solutions for finite element problems: A Fourier series expansion-based shooting method
State Key Laboratory for Strength and Vibration, Xi’an Jiaotong University（西安交通大学 强度与振动国家重点实验室）；Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology（南方科技大学 力学与航空航天工程系）
