Rotation number of contracted rotations

Abstract : 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.
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-02053125
Contributor : Aigle I2m <>
Submitted on : Friday, March 1, 2019 - 9:19:26 AM
Last modification on : Monday, March 4, 2019 - 2:04:22 PM

Links full text

Identifiers

Citation

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

Share

Metrics

Record views

19