JournalsjemsVol. 23, No. 4pp. 1053–1073

Renormalization and Siegel disks for complex Hénon maps

  • Denis Gaidashev

    Uppsala University, Sweden

  • Remus Radu

    Uppsala University, Sweden, and Romanian Academy, Bucharest, Romania

  • Michael Yampolsky

    University of Toronto, Canada
Renormalization and Siegel disks for complex Hénon maps cover
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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.

Cite this article

Denis Gaidashev, Remus Radu, Michael Yampolsky, Renormalization and Siegel disks for complex Hénon maps. J. Eur. Math. Soc. 23 (2021), no. 4, pp. 1053–1073

DOI 10.4171/JEMS/1028