Pinto's golden tilings - Almeida, João P. (2010)
We present the definition of a golden sequence. These golden sequences are Fibonacci quasi-periodic and determine a tiling of the real line. We prove the existence of a natural one-to-one correspondence between: (i) Golden sequences; (ii) Smooth conjugacy classes of circle diffeomorphisms with golden rotation number that are smooth fixed points of renormalization, and (iii) Smooth conjugacy classes of Anosov diffeomorphisms that are topologicaly conjugate to the toral automorphism G_A=(x+y,x). The Pinto-Sullivan tilings of the real line relate smooth conjugacy classes of expanding circle maps with 2-adic sequences.