Bounded Fatou components of cosine functions

2025/11/25 by Qiu, Weiyuan, Wang, Lingrui
#30D05 #37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.20010

Abstract

We constructed Yoccoz puzzle for cosine functions f(z)=ae^z+be^-z with bounded post-critical set, and proved that a Fatou component is a Jordan domains if it is bounded and is not eventually a Siegal disk. We proved that f is renormalizable if a critical value escapes to ∞. Finally, we obtained the local connectivity of J(f).

Citations

• Cubic polynomials with a parabolic point
• Proof of the Branner-Hubbard conjucture on Cantor Julia sets
• Density of periodic sources in the boundary of a basin of attraction for iteration of holomorphic maps, geometric coding trees technique
• Local connectivity of Julia sets: expository lectures

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