Rigorous bounds on the fast dynamo growth rate involving topological entropy

I. Klapper, L. S. Young

Research output: Contribution to journalArticle

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=∞.

Original languageEnglish (US)
Pages (from-to)623-646
Number of pages24
JournalCommunications In Mathematical Physics
Volume173
Issue number3
DOIs
StatePublished - Nov 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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