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The arithmetic of two-color rotations of the circle. (Russian) Zbl 1262.37022
The author discusses the relationship between one-dimensional Fibonacci tilings and dissipative (phase-space contracting) dynamical systems. A detailed account and the proofs are given in [Izv. Math. 73, No. 1, 79–120 (2009); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 73, No. 1, 79–120 (2009; Zbl 1187.37058); One-dimensional Fibonacci tilings and derivatives of two-colour rotations of a circle, Preprint MPIM2004-59, Max-Planck Inst. Math., Bonn, 2004; Izv. Math. 71, No. 2, 307–340 (2007); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 71, No. 2, 89–122 (2007; Zbl 1168.11006)].
MSC:
37E10 Dynamical systems involving maps of the circle
11B57 Farey sequences; the sequences \(1^k, 2^k, \dots\)
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
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