The geodesic flow generates a fast dynamo: an elementary proof

DOI10.1090/S0002-9939-97-04187-7zbMath0895.76096MaRDI QIDQ4372385

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Publication date: 11 December 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

constant negative curvatureunit tangent bundletwo-dimensional Riemannian manifoldmagnetic kinematic dynamo equation

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Magnetohydrodynamics and electrohydrodynamics (76W05) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (1)

Small-scale dynamo in Riemannian spaces of constant curvature

Cites Work

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• Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds
• Tangent bundle connections and the geodesic flow
• The topology of stationary curl parallel solutions of Euler's equations
• The geodesic flow and sectional curvature of pseudo-Riemannian manifolds
• The spectrum of the kinematic dynamo operator for an ideally conducting fluid
• When is an Anosov flow geodesic?
• Fast dynamo action in a steady flow
• Chaotic flows and fast magnetic dynamos
• Magnetic field generation by the motion of a highly conducting fluid

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