Limiting Laws for Entrance Times of Critical Mappings of a Circle |
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Authors: | Dzhalilov A. A. |
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Affiliation: | (1) Samarkand State University, Samarkand, Uzbekistan |
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Abstract: | A renormalization group transformation R1 has a single stable point in the space of the analytic circle homeomorphisms with a single cubic critical point and with the rotation number ( the golden mean ). Let a homeomorphism T be the C1-conjugate of . We let denote the sequence of distribution functions of the time of the kth entrance to the nth renormalization interval for the homeomorphism T. We prove that for any , the sequence has a finite limiting distribution function , which is continuous in , and singular on the interval [0,1]. We also study the sequence for k > 1. |
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Keywords: | critical homeomorphism of a circle distribution function of the entrance time thermodynamic formalism |
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