A piecewise-linear invertible noodle map
type: Item
instance of: scholarly article
title: A piecewise-linear invertible noodle map
zbMATH Open document ID: 0594.58040
DOI: 10.1016/0167-2789(84)90446-9
published in: Physica D
publication date: 1984-01-01T00:00:00Z
review text: The smooth noodle map is given by \[ (1)\quad x_{n+1}=\alpha x_ n(x^ 2_ n-1)-y_ n-z_ n,\quad y_{n+1}=\beta x_ n,\quad z_{n+1}=\gamma (x^ 2_ n-0.33)+\delta z_ n. \] The above map is of interest for its occurrence in realistic systems. But such map is not easily amenable to analysis. So the map which is amenable to analysis is the following piecewise-linear analogue \[ (2)\quad x_{n+1}=3.3(x_ n- 1)-2-y_ n-z_ n,\quad if\quad x_ n>1, \] \[ x_{n+1}=-2x_ n-y_ n-z_ n,\quad if\quad 1\geq x_ n\geq -1, \] \[ x_{n+1}=3.3(x_ n+1)+2-y_ n-z_ n,\quad if\quad x_ n<-1, \] \[ y_{n+1}=\beta x_ n,\quad z_{n+1}=\gamma (| x_ n| -1)+\delta z_ n. \] The maps (1) and (2) are invertible. The qualitative behaviour of the map (2) is discussed.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 26A18
zbMATH DE Number: 3956055
zbMATH Keywords: invertible maps
zbMATH Keywords: smooth noodle map
zbMATH Keywords: occurrence in realistic systems
author: John Lawrence Hudson
author: Otto E. Rössler
reviewed by: S. K. Chatterjea
MaRDI profile type: Publication
full work available at URL: 0167-2789(84)90446-9
OpenAlex ID: W2018843163
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description: scientific article; zbMATH DE number 3956055