Misiurewicz points on the Mandelbrot-like set concerning renormalization transformation

We study Misiurewicz points on the parameter space about a family of rational maps Tλ concerning renormalization transformation in statistical mechanic. We determine the intersection points of the Julia set J（Tλ） and the positive real axis R＋ and discuss the continuity of the Hausdorff dimension HD（...

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Veröffentlicht in:	Science China. Mathematics 2014-12, Vol.57 (12), p.2539-2548
Hauptverfasser:	Gao, JunYang, Qiao, JianYong, Zhai, Yu
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics China Continuity Hausdorff Intersections Mathematical analysis Mathematics Mathematics and Statistics Statistical mechanics Transformations (mathematics) 交叉处参数空间改造连续性重整化集合
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Zusammenfassung:	We study Misiurewicz points on the parameter space about a family of rational maps Tλ concerning renormalization transformation in statistical mechanic. We determine the intersection points of the Julia set J（Tλ） and the positive real axis R＋ and discuss the continuity of the Hausdorff dimension HD（J（f）） about real parameter ）λ.
ISSN:	1674-7283 1869-1862
DOI:	10.1007/s11425-014-4872-5