Magnetic field reversals and topological entropy in non-geodesic hyperbolic dynamos
Abstract
Earlier, Chicone, Latushkin and Montgomery-Smith [Comm Math Phys (1997)] have proved the existence of a fast dynamo operator, in compact two-dimensional manifold, as long as its Riemannian curvature be constant and negative. More recently Gallet and Petrelis [Phys Rev \textbf{E}, 80 (2009)] have investigated saddle-node bifurcation, in turbulent dynamos as modelling for magnetic field reversals. Since saddle nodes are created in hyperbolic flows, this provides us with physical motivation to investigate these reversals in a simple kinematic dynamo model obtained from a force-free non-geodesic steady flow in Lobachevsky plane. Magnetic vector potential grows in one direction and decays in the other under diffusion. Magnetic field differential 2-form is orthogonal to the plane. A restoring forcing dynamo in hyperbolic space is also given. Magnetic field reversals are obtained from this model. Topological entropies [Klapper and Young, Comm Math Phys (1995)] are also computed.
Keywords
Cite
@article{arxiv.0911.0218,
title = {Magnetic field reversals and topological entropy in non-geodesic hyperbolic dynamos},
author = {L Garcia de Andrade},
journal= {arXiv preprint arXiv:0911.0218},
year = {2009}
}