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Cerbelli and Giona's Map Is Pseudo-Anosov and Nine Consequences

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Abstract

It is shown that a piecewise affine area-preserving homeomorphism of the 2-torus studied by Cerbelli and Giona is pseudo-Anosov. This enables one to prove various of their conjectures, quantify the multifractality of its "w-measures," calculate many other quantities for its dynamics, and construct an exact area-preserving tilt map of the cylinder with proved diffusive behaviour.

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  1. Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK

    R.S. MacKay

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  1. R.S. MacKay
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MacKay, R. Cerbelli and Giona's Map Is Pseudo-Anosov and Nine Consequences. J Nonlinear Sci 16, 415–434 (2006). https://doi.org/10.1007/s00332-005-0743-0

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  • DOI: https://doi.org/10.1007/s00332-005-0743-0

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