The spectrum of the kinematic dynamo operator for an ideally conducting fluid

MOspace/Manakin Repository

Breadcrumbs Navigation

The spectrum of the kinematic dynamo operator for an ideally conducting fluid

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/9703

[+] show full item record


Title: The spectrum of the kinematic dynamo operator for an ideally conducting fluid
Author: Montgomery-Smith, Stephen, 1963-; Chicone, Carmen Charles; Latushkin, Yuri, 1956-
Keywords: Spectral mapping theorem
Riemannian manifold
Date: 2011-01-25
Abstract: The spectrum of the kinematic dynamo operator for an ideally conducting fluid and the spectrum of the corresponding group acting in the space of continuous divergence free vector fields on a compact Riemannian manifold are described. We prove that the spectrum of the kinematic dynamo operator is exactly one vertical strip whose boundaries can be determined in terms of the Lyapunov-Oseledets exponents with respect to all ergodic measures for the Eulerian flow. Also, we prove that the spectrum of the corresponding group is obtained from the spectrum of its generator by exponentiation. In particular, the growth bound for the group coincides with the spectral bound for the generator.
URI: http://hdl.handle.net/10355/9703

This item appears in the following Collection(s)

  • Mathematics publications (MU) [119]
    The items in this collection are the scholarly output of the faculty, staff, and students of the Department of Mathematics.

[+] show full item record