Hyperbolicity of Renormalization for Bi-cubic Circle Maps with Bounded Combinatorics

C. R. Math. Rep. Acad. Sci. Canada Vol. 45 (3) 2023, pp. 64–86
(Received: 2023-05-20 , Revised: 2023-10-16)

Gabriela Estevez, Instituto de Matematica e Estatıstica, Universidade Federal Fluminense, Rua Prof. Marcos Waldemar de Freitas Reis, S/N, 24.210-201, Bloco H, Campus do Gragoata, Niteroi, Rio de Janeiro RJ, Brasil; e-mail: gestevez@id.uff.br

Michael Yampolsky, Department of Mathematics, University of Toronto, 40 St George Street, Toronto, Ontario, Canada; e-mail: yampol@math.toronto.edu

Abstract/Résumé:

We construct a hyperbolic attractor of renormalization of bi-cubic circle maps with bounded combinatorics, with a codimension-two stable foliation.

On construit un attracteur hyperbolique de renormalisation pour une application de cercle bicubique à combinatoire bornée, dont la foliation est de codimension deux.

Keywords: Bi-cubic circle maps, bounded type rotation number, hyperbolicity of renormalization, renormalization operator

AMS Subject Classification: Maps of the circle, Universality; renormalization 37E10, 37E20

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