Remarks on Ruelle Operator and invariant line fields problem II

2001/10/25 by Peter Makienko, Peter M. Makienko, Makienko, Peter M.
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.math/0110272

arxiv created 2001/10/25 · openalex publication_date 2001/10/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be rational map. Critical point c is called summable if series ∑_i(1)/((Rⁱ)'(R(c))) is absolutely convergent. Under some topological condition on postcritical set we prove that R can not be structurally stable if summable critical point c ∈ J(R).

Citations

• Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality

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