Beau bounds for multicritical circle maps

Author(s)

Estevez, Gabriela ^[1] ; de Faria, Edson ^[2] ; Guarino, Pablo ^[3]

Affiliation

^[1] Univ Fed Minas Gerais, Dept Matemat, Ave Antonio Carlos 6627, BR-31270901 Belo Horizonte, MG - Brazil

^[2] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

^[3] Univ Fed Fluminense, Inst Matemat & Estat, Rua Prof Marcos Waldemar de Freitas Reis S-N, BR-24210201 Niteroi, RJ - Brazil

• Document type: Journal article
• Source: INDAGATIONES MATHEMATICAE-NEW SERIES; v. 29, n. 3, p. 842-859, JUN 2018.
• Web of Science Citations: 1

Abstract

Let f : S-1 -> S-1 be a C-3 homeomorphism without periodic points having a finite number of critical points of power-law type. In this paper we establish real a-priori bounds, on the geometry of orbits of f, which are beau in the sense of Sullivan, i.e. bounds that are asymptotically universal at small scales. The proof of the beau bounds presented here is an adaptation, to the multicritical setting, of the one given by the second author and de Melo in de Faria and de Melo (1999), for the case of a single critical point. (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 16/25053-8 - Dynamics and geometry in low dimensions
• Grantee: André Salles de Carvalho
• Support Opportunities: Research Projects - Thematic Grants