Explicit renormalisation in piecewise linear bimodal maps
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.
scientific article; zbMATH DE number 4190776