Discrete processes with dynamical and semidynamical perturbations
type: Item
instance of: scholarly article
title: Discrete processes with dynamical and semidynamical perturbations
zbMATH Open document ID: 0642.54038
DOI: 10.1016/0022-247X(88)90236-3
author: Janusz Traple
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: Let X be a compact space and \(S: X\to X\) be a homeomorphism. Let \(A: X\to L({\mathbb{R}}^ d,{\mathbb{R}}^ d)\), \(\xi\) : \(X\to {\mathbb{R}}^ d\) and \(g: {\mathbb{R}}^ d\to {\mathbb{R}}^ d\) be continuous functions. For a fixed point \(x\in X\), the difference equation \[ u(n+1)=A(S^ n(x))g(u(n))+\xi (S^ n(x))\quad (n\in {\mathbb{Z}}) \] is considered and the existence of its solutions synchronous with the motion \(S^ n(x)\) is investigated. \(\{\) Reviewer's remark: Let \(Y=X\times {\mathbb{R}}^ d\), \(p(x,u)=x\), \(F(x,u)=(S(x),A(x)g(u)+\xi (x))\). Then p: (Y,F)\(\to (X,S)\) is an extension of discrete dynamical systems [see the reviewer's book ``Extensions of minimal transformation groups'' (1979; Zbl 0431.54023)]\(\}\).
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 4046672
zbMATH Keywords: difference system
zbMATH Keywords: extension of discrete dynamical systems
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4046672