Explicit renormalisation in piecewise linear bimodal maps
type: Item
instance of: scholarly article
title: Explicit renormalisation in piecewise linear bimodal maps
zbMATH Open document ID: 0722.58040
DOI: 10.1016/0167-2789(90)90052-Q
author: D. Veitch
author: P. Glendinning
published in: Physica D
publication date: 1990-01-01T00:00:00Z
review text: The authors study here the following two-parameter families of piecewise linear maps: \[ \begin{alignedat}{2} T_{b,t} &= t(x+b)+2, &&\qquad x<-(b+1/t), \\ T_{b,t} &= -t(x+b), &&\qquad -(b+1/t)\leq x\leq 1/t-b, \\ T_{b,t} &= t(x+b)-2, &&\qquad x>1/t-b,\end{alignedat} \] which arises naturally in the study of general bimodal maps and \[ \begin{alignedat}{2} S_{p,m}(x) &= m(x+1/p)+1, &&\qquad x<-1/p, \\ S_{p,m}(x) &= -px &&\qquad -1/p \leq x\leq 1/p, \\ S_{p,m}(x) &= m(x-1/p)-1, &&\qquad x>1/p,\end{alignedat} \] which is a special case of a bimodal piecewise, linear map having been discussed in relation to pulse-modulation feedback problems in control theory. The dynamics of these maps is characterized by describing their non- wandering sets as a function of the parameters.
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 54C70
zbMATH DE Number: 4190776
zbMATH Keywords: non-wandering set
zbMATH Keywords: bimodal piecewise, linear map
MaRDI profile type: Publication
cites work: Q3814426
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description: scientific article; zbMATH DE number 4190776