### 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) |
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Pages (from-to) | 623-646 |

Number of pages | 24 |

Journal | Communications In Mathematical Physics |

Volume | 173 |

Issue number | 3 |

DOIs | |

State | Published - Nov 1995 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Klapper, I., & Young, L. S. (1995). Rigorous bounds on the fast dynamo growth rate involving topological entropy.

*Communications In Mathematical Physics*,*173*(3), 623-646. https://doi.org/10.1007/BF02101659