2002/01/21 by Patricia Domínguez, P. Domínguez, Domínguez, P. +6
Mathematics · #37F10: 37F45 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Stochastic processes and statistical mechanics #math.CV #math.DS #msc:37F45
paper · pdf · doi:10.48550/arxiv.math/0201200
arxiv created 2002/01/21 · openalex publication_date 2002/01/21 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If f is a transcendental entire function with only algebraic singularities we calculate the Ruelle operator of f. Moreover, we prove both (i) if f has a summable critical point, then f is not structurally stable under certain topological conditions and (ii) if all critical points of f belonging to Julia set are summable, then there exists no invariant lines fields in the Julia set.