2006/09/07 by Hadda Hmili, Hmili, Hadda · 1 citation
Computer Science · Mathematics · #37A25 37E05 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:37A25 #msc:37E05
paper · pdf · doi:10.48550/arxiv.math/0609192
13 pages, 6 figures
arxiv created 2006/09/07 · openalex publication_date 2006/09/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove a criterion for existence of continuous non constant eigenfunctions for interval exchange transformations, that is for non topologically weak mixing. We first construct, for any m>3, uniquely ergodic interval exchange transformations of rank 2 with irrational eigenvalues associated to continuous eigenfunctions, so that are not topologically weak mixing, this answers to a question of Ferenczi and Zamboni. Then, we construct, for any even number m>3, interval exchange transformations of rank 2 with both irrational eigenvalues (associated to continuous eigenfunctions) and non trivial rational eigenvalues (associated to piecewise continuous eigenfunctions). Moreover these examples can be chosen to be either uniquely ergodic or non minimal.