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Proceedings of the American Mathematical Society

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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: 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