Dynamical Systems Seminar-On Penrose tilings and tiling dynamical systems: VI

Abstract: The set of Penrose tilings is “almost” parameterized by a 4-torus. The R^2 translation action is product of a pair of suspensions of Sturmian dynamical systems. The inflation map is (almost) a hyperbolic total automorphism, with the Markov partition drawing the Penrose tiles.