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Renormalization group analysis of quasi-periodicity in analytic maps

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Abstract

Analytic maps of the form\(f(z) = e^{2\pi i\Omega } z + \mathcal{O}(z^2 )\) display quasiperiodicity when Ω satisfies a diophantine condition. Quasiperiodic motion is confined to a neighborhood of the origin known as a Siegel domain. The boundary of this domain obeys universal scaling relations. In this paper we investigate these scaling relations through a renormalization group analysis, and we discuss singularities and asymptotic form of the scaling function.

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Author notes

  1. Michael Widom

    Present address: Department of Physics, Harvard University, 02138, Cambridge, MA, USA

Authors and Affiliations

  1. The James Franck Institute and The Department of Physics, The University of Chicago, 60637, Chicago, IL, USA

    Michael Widom

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  1. Michael Widom
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Additional information

Communicated by O. E. Lanford

A thesis submitted to the Department of Physics, University of Chicago, Chicago, Illinois, in partial fulfillment of the requirements for the Ph.D. degree

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Widom, M. Renormalization group analysis of quasi-periodicity in analytic maps. Commun.Math. Phys. 92, 121–136 (1983). https://doi.org/10.1007/BF01206316

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  • DOI: https://doi.org/10.1007/BF01206316

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