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Publication
Pinto's golden tilings
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Authors
Advisor(s)
Abstract(s)
We present an one-to-one correspondence between (i) Pinto's golden tilings;
(ii) smooth conjugacy classes of golden di eomorphism of the circle that are
xed points of renormalization; (iii) smooth conjugacy classes of Anosov difeo-
morphisms, with an invariant measure absolutely continuous with respect to
the Lebesgue measure, that are topologically conjugated to the Anosov au-
tomorphism G(x; y) = (x + y; x); (iv) solenoid functions. As we will explain,
the solenoid functions give a parametrization of the in nite dimensional space
consisting of the mathematical objects described in the above equivalences.
Description
Keywords
Anosov diffeomorphisms Arc exchange systems Renormalization Tilings Train tracks
Citation
Almeida, João P. (2010). Pinto's golden tilings. In Discrete Dynamics and Difference Equations: Proceedings of the Twelfth International Conference on Difference Equations and Applications.