Almeida, João P.2018-04-302018-04-302015Almeida, João P. (2015). Anosov diffeomorphisms and tilings. In International Workshop Progress on Difference Equations. Universidade da Beira Interior, Covilhãhttp://hdl.handle.net/10198/17426We consider a toral Anosov automorphism G : T → T given by G(x, y) = (ax + y; x), where a > 1 is a fixed integer, and introduce the notion of γ-tiling to prove the existence of a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms with invariant measure absolutely continuous with respect to the Lebesgue measure and topologically conjugate to G, (ii) affine classes of - tilings and (iii) solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences. This talk is based on a joint work with Alberto PintoengDynamical systemsAnosov diffeomorphismsTilingsconference object