Infinite-dimensional Thurston theory and transcendental dynamics IV:\n dependence on parameters and escape on (pre-)periodic rays

2021/04/27 by Константин Богданов, Bogdanov, Konstantin, Konstantin Bogdanov
Mathematics · #37F10 (Primary) 37F12 #37F20 (Secondary) #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2104.13102

openalex publication_date 2021/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider transcendental entire functions that are compositions of a\npolynomial and the exponential for which all singular values escape on disjoint\nrays. Based on their classification in [B3] we investigate their dependence on\nparameters, that is, on the potentials and external addresses of singular\nvalues. Using continuity argument we generalize the classification in [B3] to\nthe case when dynamic rays containing singular values are (pre-)periodic.\n

Citations

• Infinite-dimensional Thurston theory and transcendental dynamics II: classification of entire functions with escaping singular orbits
• Infinite-dimensional Thurston theory and transcendental dynamics III: entire functions with escaping singular orbits in the degenerate case

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