Beltrami fields with hyperbolic periodic orbits enclosed by knotted invariant tori

DOI10.1016/j.aim.2020.107328OpenAlexW3047117997WikidataQ115598705 ScholiaQ115598705MaRDI QIDQ2196631

Alejandro Luque, Alberto Enciso, Daniel Peralta-Salas

Publication date: 3 September 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.07448

zbMATH Keywords

KAM theoryinvariant toriBeltrami fieldsMelnikov theoryfluid flows

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (7)

Beltrami fields and knotted vortex structures in incompressible fluid flows ⋮ Beltrami fields exhibit knots and chaos almost surely ⋮ Geometric hydrodynamics in open problems ⋮ Steady Euler flows on \({\mathbb{R}}^3\) with wild and universal dynamics ⋮ Nested invariant tori foliating a vector field and its curl: Toward MHD equilibria and steady Euler flows in toroidal domains without continuous Euclidean isometries ⋮ On the global stability of smooth solutions of the Navier-Stokes equations ⋮ An improved Liouville type theorem for Beltrami flows

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