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