Towards a Realistic Fast Dynamo: Models Based on Cat Maps and Pseudo-Anosov Maps

Fast dynamo models based on cat maps with shear are introduced. With an appropriate choice of shear even and odd magnetic fields evolve independently. Fast dynamo action occurs for even fields in the absence of shear; the introduction of shear introduces cancellations and modifies growth rates. An odd field may be considered as lying in a disc and evolving under a pseudo-Anosov map, which stretches and folds field but does not reconnect field lines. Without shear odd fields decay, but non-trivial shear allows fast amplification of field by the stretch-fold-shear mechanism. Numerical evidence is presented showing that these models can act as fast dynamos for both even and odd fields. The limit of large stretching by the cat map is considered and proofs of fast dynamo action in this limit are presented.