Golden tilings

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

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

Golden tilings
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by A. A. Pinto, J. P. Almeida and A. Portela PDF

Trans. Amer. Math. Soc. 364 (2012), 2261-2280 Request permission

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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