Poincaré's recurrence theorems for set-valued dynamical systems
type: Item
instance of: scholarly article
title: Poincaré's recurrence theorems for set-valued dynamical systems
zbMATH Open document ID: 0899.54027
DOI: 10.1016/S0893-9659(97)00102-X
author: J. Ning
published in: Applied Mathematics Letters
publication date: 1998-11-11T00:00:00Z
review text: Given two topological spaces \(X\) and \(Y\), the authors define a `set-valued dynamical system' as a map \(F:X \to 2^Y\). When \(X=Y\), a notion of `an invariant measure' is defined and it is shown that if \(X\) is a metric space and \(F\) is a compact, upper semi-continuous map with non-empty closed values then the system \((X,F)\) admits an `invariant measure'. Given two set-valued dynamical systems \(F_1: X\to 2^Y\) and \(F_2: Y\to 2^X\) (where \(X\) and \(Y\) are metric spaces) the authors define a notion of `a pair of coincident invariant measures' and prove their existence under certain conditions. Furthermore, they formulate and prove a version of Poincaré recurrence result in their set-up.
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 28C10
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 1106436
zbMATH Keywords: set valued dynamical systems
zbMATH Keywords: Poincaré recurrence
reviewed by: Mahesh Nerurkar
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1106436