Constructive QP-Time-dependent KAM Algorithm for Lagrangian Tori
Dynamical Systems
2025-04-02 v1
Abstract
In this paper, we present an algorithm to computea fiberwise Lagrangian torus in quasi-periodic (QP) Hamiltonian systems, whose convergence is proved in the [CHP25]. We exhibit the algorithm with two models. The first is a Tokamak model [CVC+05, VL21], which proposes a control method to create barriers to the diffusion of magnetic field lines through a small modification in the magnetic perturbation. The second model [dCN00], known as the vorticity defect model, describes the nonlinear evolution of localized vorticity perturbations in a constant vorticity flow. This model was originally derived in the context of plasma physics and fluid dynamics.
Cite
@article{arxiv.2504.00335,
title = {Constructive QP-Time-dependent KAM Algorithm for Lagrangian Tori},
author = {Renato Calleja and Alex Haro and Pedro Porras},
journal= {arXiv preprint arXiv:2504.00335},
year = {2025}
}