On functional equations associated with the renormalization of non-commuting circle mappings

Christodoulides, Y. T. and Mestel, B. D. (2007). On functional equations associated with the renormalization of non-commuting circle mappings. Journal of Physics A: Mathematical and Theoretical, 40(39) pp. 11877–11897.

DOI: https://doi.org/10.1088/1751-8113/40/39/012

Abstract

We investigate the functional equations associated with critical non-commuting circle homeomorphisms. Using Epstein's Herglotz function methods, we show that there are analytic solutions of a class of functional equations closely related to period-two points of the circle-map renormalization transformations for rotation number with continued fraction [p, p,...], p epsilon N.

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