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Misiurewicz points on the Mandelbrot-like set concerning renormalization transformation

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Abstract

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

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Authors and Affiliations

  1. School of Science, China University of Mining and Technology, Beijing, 100083, China

    JunYang Gao, JianYong Qiao & Yu Zhai

  2. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    JianYong Qiao

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  1. JunYang Gao
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  2. JianYong Qiao
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  3. Yu Zhai
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Correspondence to JunYang Gao.

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Gao, J., Qiao, J. & Zhai, Y. Misiurewicz points on the Mandelbrot-like set concerning renormalization transformation. Sci. China Math. 57, 2539–2548 (2014). https://doi.org/10.1007/s11425-014-4872-5

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  • DOI: https://doi.org/10.1007/s11425-014-4872-5

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