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      Beau bounds for multicritical circle maps

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          Abstract

          Let \(f: S^1\to S^1\) 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, for the case of a single critical point.

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          Sur la Conjugaison Différentiable des Difféomorphismes du Cercle a des Rotations

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            Author and article information

            Journal
            2016-11-02
            Article
            1611.00722
            6dc972b4-caba-43f7-9496-01ffe46a7e9f

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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            Eighteen pages. This work is a continuation of the article https://arxiv.org/abs/1511.09056, by the first two authors
            math.DS

            Differential equations & Dynamical systems
            Differential equations & Dynamical systems

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