Golden tilings

Pinto, A.; Almeida, J.; Portela, A.

doi:10.1090/S0002-9947-2011-05293-1

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
DOI: https://doi.org/10.1090/S0002-9947-2011-05293-1
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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