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arXiv · 2504.00335

Constructive QP-Time-dependent KAM Algorithm for Lagrangian Tori

Renato Calleja·Alex Haro·Pedro Porras
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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.

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Renato Calleja, Alex Haro, Pedro Porras. 2025-04-01. Constructive QP-Time-dependent KAM Algorithm for Lagrangian Tori. https://arxiv.org/abs/2504.00335

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