RIGOROUS BOUNDS ON THE FAST DYNAMO GROWTH-RATE INVOLVING TOPOLOGICAL-ENTROPY

The fast dynamo growth rate for a C-k+1 map or flow is bounded above b y topological entropy plus a l/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-d ynamo theorem: in C-infinity systems fast dynamo action is not possibl e without the presence of chaos. In addition topological entropy is us ed to construct a lower bound for the fast dynamo growth rate in the c ase R(m) = infinity.