Deformation of invariant tori under perturbation

• DOI: 10.48550/arxiv.2407.06440
• Publication Date: 2024-07-08
• Authors: W. Wei; Jiankun Hua; A. Knieps; Y. Liang
• Keywords: Plasma Physics (physics.plasm-ph); FOS: Mathematics; FOS: Physical sciences; Dynamical Systems (math.DS); Mathematics - Dynamical Systems; Chaotic Dynamics (nlin.CD); Nonlinear Sciences - Chaotic Dynamics; Physics - Plasma Physics; Primary: 37D10, Secondary: 34D10, 37N05, 37N10, 37M21, 37J40, 39A33, 39B52, 76W05, 78M30

This study extends the functional perturbation theory, originally developed for orbits and periodic in dynamical systems, \textit{e.g.} a map $\mathcal{P}$, to derive formulae deformation of an $d$-dimensional invariant torus, on which one can define $\mathcal{P}^k$ $k\in \mathbb{R}$ even $\mathbf{k}\in\mathbb{R}^d$ continuize generalize exponential function $\mathcal{P}^{\mathbf{k}}$ $k$. The tori, manifest as closed flux surfaces magnetic confinement fusion (MCF) machines, are dominant structure influencing radial transport and, consequently, overall performance.