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

• Autores: R. S. MacKay
• Localización: Journal of nonlinear science, ISSN 0938-8974, Vol. 16, Nº 4, 2006, págs. 415-434
• Idioma: inglés
• DOI: 10.1007/s00332-005-0743-0
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• Resumen

  • 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.