This article is cited in 2 papers

Golden mean Siegel disk universality and renormalization

Denis Gaidashev^a, Michael Yampolsky<sup>b

a</sup> Uppsala University, Uppsala, Sweden
^b University of Toronto, Toronto, Canada

Abstract: We provide a computer-assisted proof of one of the central open questions in one-dimensional renormalization theory – universality of the golden-mean Siegel disks. We further show that for every function in the stable manifold of the golden-mean renormalization fixed point the boundary of the Siegel disk is a quasicircle which coincides with the closure of the critical orbit, and that the dynamics on the boundary of the Siegel disk is rigid. Furthermore, we extend the renormalization from one-dimensional analytic maps with a golden-mean Siegel disk to two-dimensional dissipative Hénon-like maps and show that the renormalization hyperbolicity result still holds in this setting.

Key words and phrases: renormalization, universality, Siegel disk, Henon-like map.

MSC: 37E20, 37F25, 37F50, 37F80

Language: English

DOI: 10.17323/1609-4514-2022-22-3-451-491