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