Rigorous bounds on the fast dynamo growth rate involving topological entropy |
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| Authors: | I. Klapper L. S. Young |
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| Affiliation: | (1) Program in Applied Mathematics, University of Arizona, 85721 Tucson, AZ, USA;(2) Department of Mathematics, University of California, 90024 Los Angeles, CA, USA |
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| Abstract: | The fast dynamo growth rate for aCk+1 map or flow is bounded above by topological entropy plus a 1/k correction. The proof uses techniques of random maps combined with a result of Yomdin relating curve growth to topological entropy. This upper bound implies the following anti-dynamo theorem: inC systems fast dynamo action is not possible without the presence of chaos. In addition topological entropy is used to construct a lower bound for the fast dynamo growth rate in the caseRm=.This author is supported by an NSF postdoctoral fellowshipThis author is partially supported by an NSF grant |
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