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=∞.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics