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Article Dans Une Revue Journal of modern dynamics Année : 2018

Rotation number of contracted rotations

Résumé

Let 0 < lambda< 1. We consider the one-parameter family of circle lambda-affine contractions f(delta): x is an element of [0,1] -> lambda x + delta mod 1, where 0 <= delta < 1. Let rho be the rotation number of the map f(delta). We will give some numerical relations between the values of lambda,delta and rho, essentially using Hecke-Mahler series and a tree structure. When both parameters lambda and delta are algebraic numbers, we show that rho is a rational number. Moreover, in the case lambda and delta are rational, we give an explicit upper bound for the height of rho under some assumptions on lambda.

Dates et versions

hal-02053125 , version 1 (01-03-2019)

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Michel Laurent, Arnaldo Nogueira. Rotation number of contracted rotations. Journal of modern dynamics, 2018, 12 (1), pp.175-191. ⟨10.3934/jmd.2018007⟩. ⟨hal-02053125⟩
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