Rigorous bounds on the fast dynamo growth rate involving topological entropy

I. Klapper; L. S. Young

doi:10.1007/BF02101659

Rigorous bounds on the fast dynamo growth rate involving topological entropy

I. Klapper, L. S. Young

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The fast dynamo growth rate for a C^k+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: in C^∞ 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 case R_m=∞.

Original language	English (US)
Pages (from-to)	623-646
Number of pages	24
Journal	Communications In Mathematical Physics
Volume	173
Issue number	3
DOIs	https://doi.org/10.1007/BF02101659
State	Published - Nov 1995

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02101659

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abstract = "The fast dynamo growth rate for a Ck+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: in C∞ 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 case Rm=∞.",

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AB - The fast dynamo growth rate for a Ck+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: in C∞ 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 case Rm=∞.

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Rigorous bounds on the fast dynamo growth rate involving topological entropy

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