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Authors
Advisor(s)
Abstract(s)
We present the definition of a golden sequence. These golden sequences are Fibonacci
quasi-periodic and determine a tiling of the real line. We prove the existence
of a natural one-to-one correspondence between: (i) Golden sequences;
(ii) Smooth conjugacy classes of circle diffeomorphisms with golden rotation
number that are smooth fixed points of renormalization, and (iii) Smooth conjugacy
classes of Anosov diffeomorphisms that are topologicaly conjugate to
the toral automorphism G_A=(x+y,x). The Pinto-Sullivan tilings of the real
line relate smooth conjugacy classes of expanding circle maps with 2-adic sequences.
Description
Keywords
Golden tilings Renormalization Anosov diffeomorphisms
Pedagogical Context
Citation
Almeida, João P. (2010). Pinto's golden tilings. In EURO XXIV. Lisboa, Portugal