Golden mean renormalization for a generalized Harper equation: The Ketoja–Satija orchid

Mestel, B. D. and Osbaldestin, A. H. (2004). Golden mean renormalization for a generalized Harper equation: The Ketoja–Satija orchid. Journal of Mathematical Physics, 45(12) pp. 5042–5075.

DOI: https://doi.org/10.1063/1.1797532

Abstract

We provide a rigorous analysis of the fluctuations of localized eigenstates in a generalized Harper equation with golden mean flux and with next-nearest-neighbor interactions. For next-nearest-neighbor interaction above a critical threshold, these self-similar fluctuations are characterized by orbits of a renormalization operator on a universal strange attractor, whose projection was dubbed the "orchid" by Ketoja and Satija [Phys. Rev. Lett. 75, 2762 (1995)]. We show that the attractor is given essentially by an embedding of a subshift of finite type, and give a description of its periodic orbits.

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