Renormalization of correlations in a quasiperiodically forced two-level system: quadratic irrationals

Mestel, B. D. and Osbaldestin, A. H. (2004). Renormalization of correlations in a quasiperiodically forced two-level system: quadratic irrationals. Journal of Physics A: Mathematical and General, 37(38) pp. 8969–8989.

DOI: https://doi.org/10.1088/0305-4470/37/38/005

Abstract

Generalizing from the case of golden mean frequency to a wider class of quadratic irrationals, we extend our renormalization analysis of the self-similarity of correlation functions in a quasiperiodically forced two-level system. We give a description of all piecewise-constant periodic orbits of an additive functional recurrence generalizing that present in the golden mean case. We establish a criterion for periodic orbits to be globally bounded, and also calculate the asymptotic height of the main peaks in the correlation function.

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