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We consider a toral Anosov automorphism G(gamma) : T-gamma --> T-gamma given by G(gamma) (x, y) = (ax + y, x) in the < v, w > base, where , a is an element of N\{1}, gamma = 1/(a + 1/(a + 1/...)), v = (gamma, 1) and w = (-1, gamma) in the canonical base of R-2 and T-gamma = R-2 / (vZ x wZ). We introduce the notion of gamma-tilings to prove the existence of a one-to-one correspondence between (i) marked smooth conjugacy classes of Anosov diffeomorphisms, with invariant measures absolutely continuous with respect to the Lebesgue measure, that are in the isotopy class of G(gamma); (ii) affine classes of gamma-tilings; and (iii) gamma-solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences.

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For Anosov flows obtained by suspensions of Anosov diffeomorphisms on surfaces, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point, then the conjugacy has a smooth extension to the suspended 3-manifold. This result generalizes the similar ones of Sullivan and Ferreira-Pinto for 1-dimensional expanding dynamics and also a result of Ferreira-Pinto for 2-dimensional hyperbolic dynamics.

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This paper presents the main concepts and results of a Master thesis in Data Analysis which aims to analyze the evolution of some developed countries and also of some emerging countries that are members of the Organisation for Economic Co-operation and Development (OECD) in what concerns some indicators or variables of well-being during the period 2011-2015, through the STATIS (Structuring Three-way data sets in Statistics) methodology. This methodology allows to analyze the presence of a common structure in several data tables obtained over time, to identify the differences and similarities along the period of time under study and according to well-being indicators included in the "Your Better Life Index" of the OECD, and to analyze the trajectories of the countries.

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