2012/03/21 by Charlene Kalle, CHARLENE KALLE
Mathematics · #Advanced Differential Equations and Dynamical Systems #Constant (computer programming) #Existential quantification #Isomorphism (crystallography) #Mathematical Dynamics and Fractals #Mathematics and Applications #Piecewise #Piecewise linear function #Set (abstract data type) #math.DS #msc:11K55 #msc:37A05 #msc:37A35
paper · pdf · doi:10.1017/etds.2012.127
published as Ergod. Th. Dynam. Sys. 34 (2014) 153-170 · 18 pages, 8 figures
arxiv created 2012/03/21 · openalex publication_date 2012/11/09 · openalex created_date 2016/06/24 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/05
Abstract We compare a piecewise linear map with constant slope β \gt 1 and a piecewise linear map with constant slope -β . These maps are called the positive and negative β -transformations. We show that for a certain set of β s, the multinacci numbers, there exists a measurable isomorphism between these two maps. We further show that for all other values of β between 1 and 2 the two maps cannot be isomorphic.