Anosov and circle diffeomorphisms - J. P. Almeida (2011)
We present an infinite dimensional space of $C^{1+}$  smooth conjugacy classes of circle diffeomorphisms that are C^{1+}  fixed points of renormalization. We exhibit a one-to-one correspondence between these C^{1+} fixed points of renormalization and C^{1+}  conjugacy classes of Anosov diffeomorphisms.