Limiting Laws for Entrance Times of Critical Mappings of a Circle期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Limiting Laws for Entrance Times of Critical Mappings of a Circle

Authors:	Dzhalilov A. A.

Affiliation:	(1) Samarkand State University, Samarkand, Uzbekistan

Abstract:	A renormalization group transformation R₁ has a single stable point $T_{xi _0 ,eta _0 }$ 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 $T_{xi _0 ,eta _0 }$ . We let ${ Phi _n^{(k)} (t),n = overline {1,infty } }$ 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 $t in mathbb{R}^1$ , the sequence ${ Phi _n^{(1)} (t)}$ has a finite limiting distribution function $Phi ^{(1)} (t)$ , which is continuous in $mathbb{R}^1$ , and singular on the interval [0,1]. We also study the sequence ${ Phi _n^{(k)} (t),n = overline {1,infty } }$ for k>1.

Keywords:	critical homeomorphism of a circle distribution function of the entrance time thermodynamic formalism
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