Steady Euler Flows on $${\mathbb {R}}^3$$ with Wild and Universal Dynamics

Berger, Pierre; Florio, Anna; Peralta‐Salas, Daniel

doi:10.1007/s00220-023-04660-6

Commun. Math. Phys.

2023

DOI: 10.1007/s00220-023-04660-6

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Steady Euler Flows on $${\mathbb {R}}^3$$ with Wild and Universal Dynamics

Pierre Berger

Anna Florio

Daniel Peralta‐Salas

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2024

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Cited by 2 publications

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Obstructions to Topological Relaxation for Generic Magnetic Fields

Enciso,

Peralta-Salas

2024

Arch Rational Mech Anal

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For any (analytic) axisymmetric toroidal domain $$\Omega \subset \mathbb {R}^3$$ Ω ⊂ R 3 we prove that there is a locally generic set of divergence-free vector fields that are not topologically equivalent to any magnetohydrostatic (MHS) state in $$\Omega $$ Ω . Each vector field in this set is Morse–Smale on the boundary, does not admit a nonconstant first integral, and exhibits fast growth of periodic orbits; in particular this set is residual in the Newhouse domain. The key dynamical idea behind this result is that a vector field with a dense set of nondegenerate periodic orbits cannot be topologically equivalent to a generic MHS state. On the analytic side, this geometric obstruction is implemented by means of a novel rigidity theorem for the relaxation of generic magnetic fields with a suitably complex orbit structure.

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Obstructions to Topological Relaxation for Generic Magnetic Fields

Enciso,

Peralta-Salas

2024

Arch Rational Mech Anal

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Force-Free Fields Are Conformally Geodesic

Chern,

Gross

2024

SIAM J. Appl. Algebra Geometry

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Steady Euler Flows on $${\mathbb {R}}^3$$ with Wild and Universal Dynamics

Cited by 2 publications

References 53 publications

Obstructions to Topological Relaxation for Generic Magnetic Fields

Obstructions to Topological Relaxation for Generic Magnetic Fields

Force-Free Fields Are Conformally Geodesic

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