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A decomposition theorem for Herman maps

2012/03/26 by Xiaoguang Wang, Wang, Xiaoguang
Computer Science · Mathematics · #37F20 #37F30 #37F50 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1203.5563

openalex publication_date 2012/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1980s, Thurston established a topological characterization theorem for postcritically finite rational maps. In this paper, a decomposition theorem for a class of postcritically infinite branched covering termed `Herman map' is developed. It's shown that every Herman map can be decomposed along a stable multicurve into finitely many Siegel maps and Thurston maps, such that the combinations and rational realizations of these resulting maps essentially dominate the original one. This result gives an answer to a problem of McMullen in a sense and enables us to prove a Thurston-type theorem for rational maps with Herman rings.

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