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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Golden tilings

Authors: A. A. Pinto, J. P. Almeida and A. Portela
Journal: Trans. Amer. Math. Soc. 364 (2012), 2261-2280
MSC (2000): Primary 37C15; Secondary 37C40
Published electronically: December 16, 2011
MathSciNet review: 2888206
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Abstract: We introduce the notion of golden tilings, and we prove a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, (ii) affine classes of golden tilings and (iii) solenoid functions. The solenoid functions give a parametrization of the infinite dimensional space consisting of the mathematical objects described in the above equivalences.

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Additional Information

A. A. Pinto
Affiliation: Departamento de Matemática e LIAAD-INESC Porto LA, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal

J. P. Almeida
Affiliation: Escola Superior de Tecnologia e de Gestão, Instituto Politécnico de Bragança, Campus de Santa Apolónia, Ap. 1134, 5301-854 Bragança, Portugal

A. Portela
Affiliation: Instituto de Matemática, Facultad de Ingenieria, CC30, CP 11300, Universidad de la Republica, Montevideo, Uruguay

PII: S 0002-9947(2011)05293-1
Keywords: Anosov diffeomorphisms, circle diffeomorphisms, dynamics, renormalization, solenoid functions, tilings
Received by editor(s): February 21, 2008
Received by editor(s) in revised form: January 5, 2010
Published electronically: December 16, 2011
Article copyright: © Copyright 2011 American Mathematical Society