1111-37-703 Jo˜ao P. Almeida* ([email protected]), Escola Superior de

1111-37-703
João P. Almeida* ([email protected]), Escola Superior de Tecnologia e Gestão, Campus de Santa
Apolónia, Ap. 1145, 5301-875 Bragança, Portugal, and Alberto A. Pinto ([email protected]),
Department of Mathematics, Faculty of Sciences, Rua Campo Alegre 687, 4169-007 Porto,
Portugal. Anosov diffeomorphisms and tilings.
We consider a toral Anosov automorphism Gγ : T → T given by Gγ (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 Gγ , (ii) affine classes of γ-tilings and (iii) solenoid functions. Solenoid functions provide a
parametrization of the infinite dimensional space of the mathematical objects described in these equivalences. (Received
February 10, 2015)
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