37F80 — 1 articles found.

KAM-renormalization and Herman Rings for 2D Maps

C. R. Math. Rep. Acad. Sci. Canada Vol. 43 (2) 2021, pp. 78-86
Vol.43 (2) 2021
Michael Yampolsky Details
(Received: 2021-03-14 , Revised: 2021-04-21 )
(Received: 2021-03-14 , Revised: 2021-04-21 )

Michael Yampolsky, Department of Mathematics, University of Toronto, Toronto, ON, Canada M5S 2E4; e-mail: yampol@math.toronto.edu


In this note, we extend the renormalization horseshoe we have recently constructed with N. Goncharuk for analytic diffeomorphisms of the circle to their small two-dimensional perturbations. As one consequence, Herman rings with rotation numbers of bounded type survive on a codimension one set of parameters under small two-dimensional perturbations.

On étend le fer à cheval de renormalisation récemment construit avec N. Goncharuk pour les difféomorphismes analytiques du cercle à leurs petites perturbations à deux dimensions. Il suit que les anneaux de Herman à nombre de rotation de type borné survivent sur un ensemble de paramètres à codimension un sous petites perturbations à deux dimensions.

Keywords: Henon-like maps, Herman rings, rotation domains

AMS Subject Classification: Renormalization, Small divisors; rotation domains and linearization; Fatou and Julia sets, 37F25, 37F50, 37F80

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