Pinto's Golden Tilings

Abstract

We present an one-to-one correspondence between (i) Pinto’s golden tilings; (ii) smooth conjugacy classes of golden diffeomorphism of the circle that are fixed points of renormalization; (iii) smooth conjugacy classes of Anosov difeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, that are topologically conjugated to the Anosov automorphism G(x, y) = (x + y, x); (iv) solenoid functions. As we will explain, the solenoid functions give a parametrization of the infinite dimensional space consisting of the mathematical objects described in the above equivalences.