The geodesic flow generates a fast dynamo:

an elementary proof

Authors:
C. Chicone and Y. Latushkin

Journal:
Proc. Amer. Math. Soc. **125** (1997), 3391-3396

MSC (1991):
Primary 76W05, 58F99, 58G25

DOI:
https://doi.org/10.1090/S0002-9939-97-04187-7

MathSciNet review:
1443147

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Abstract | References | Similar Articles | Additional Information

Abstract: We give elementary and explicit arguments to show that the geodesic flow on the unit tangent bundle of a two dimensional Riemannian manifold with constant negative curvature provides an example of a ``fast'' dynamo for the magnetic kinematic dynamo equation.

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Additional Information

**C. Chicone**

Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211

Email:
carmen@chicone.math.missouri.edu

**Y. Latushkin**

Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211

Email:
yuri@math.missouri.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-04187-7

Keywords:
Kinematic dynamo,
geodesic flow

Received by editor(s):
April 24, 1996

Additional Notes:
The first author’s research was supported by the National Science Foundation under the grant DMS-9303767; the second author was supported by the National Science Foundation under the grant DMS-9400518 and by the SRF of the University of Missouri.

Communicated by:
Jeffrey B. Rauch

Article copyright:
© Copyright 1997
American Mathematical Society