Beltrami fields with hyperbolic periodic orbits enclosed by knotted\n invariant tori

2019/09/16 by Alberto Enciso, Alejandro Luque, Enciso, Alberto +3
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1909.07448

openalex publication_date 2019/09/16 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We prove that there exist Beltrami fields in Euclidean space, with sharp\ndecay at infinity, which have a prescribed set of invariant tori (possibly\nknotted or linked) that enclose an arbitrarily large number of hyperbolic\nperiodic orbits. These hyperbolic orbits are cablings over the core curve of\neach torus. Moreover, the domain bounded by each invariant torus is covered by\nan almost full measure set of invariant tori. We show that an analogous result\nholds for high-frequency Beltrami fields on the flat 3-torus.\n

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