Rigorous Bounds on the Fast Dynamogrowth Rate
نویسندگان
چکیده
The fast dynamo growth rate for a C k+1 map or ow is bounded above by topo-logical 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 1 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 = 1.
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The fast dynamo growth rate for a C k+1 map or ow is bounded above by topo-logical 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 1 systems fast dynamo action is not possible without the presence of chaos. In addition topologica...
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