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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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