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Renormalization and Siegel disks for complex Hénon maps

2016/04/24 by Gaidashev, Denis, Radu, Remus, Yampolsky, Michael
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.07069

Abstract

We use hyperbolicity of golden-mean renormalization of dissipative Hénon-like maps to prove that the boundaries of Siegel disks of sufficiently dissipative quadratic complex Hénon maps with golden-mean rotation number are topological circles. Conditionally on an appropriate renormalization hyperbolicity property, we derive the same result for Siegel disks of Hénon maps with all eventually periodic rotation numbers.

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