Magnetic field reversals and topological entropy in non-geodesic hyperbolic dynamos

TL;DR

This paper investigates magnetic field reversals in hyperbolic dynamo models derived from non-geodesic flows on the Lobachevsky plane, analyzing topological entropy and demonstrating reversals through a simplified kinematic dynamo approach.

Contribution

It introduces a new hyperbolic dynamo model based on non-geodesic flows and analyzes magnetic reversals and topological entropy within this framework.

Findings

Magnetic field reversals are demonstrated in the hyperbolic dynamo model.

Topological entropy of the system is computed, indicating chaotic behavior.

A restoring forcing dynamo in hyperbolic space is also presented.

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.