Invariant measures of differential inclusions applied to singular perturbations
type: Item
instance of: scholarly article
title: Invariant measures of differential inclusions applied to singular perturbations
zbMATH Open document ID: 0923.34013
published in: Journal of Differential Equations
publication date: 1999-10-18T00:00:00Z
review text: Generalizing the well-known classical concepts and results concerning invariant measures for dynamical systems in [\textit{N. Kryloff} and \textit{N. Bogoliouboff}, Ann. Math., II. Ser. 38, 65-113 (1937; Zbl 0016.08604); \textit{V. V. Nemytskii} and \textit{V. V. Stepanov}, Qualitative theory of differential equations, Princeton Univ. Press (1960; Zbl 0089.29502)], the author introduces two concepts of invariant measure (``occupational'' and, respectively, ``projectional'') for the solutions to an autonomous compact and convex-valued differential inclusion of the form: \(y'\in G(y)\subset \mathbb{R}^n\), in particular for differential equations without uniqueness. This very consistent and clearly written article contains a large number of results concerning the equivalence of two concepts of invariant measures, their basic properties and relevant applications to singularly perturbed differential inclusions of the form: \((x',\varepsilon y')\in G(x,y)\).
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 1283665
zbMATH Keywords: differential inclusion
zbMATH Keywords: occupational invariant measure
zbMATH Keywords: projectional invariant measure
zbMATH Keywords: singular perturbation
reviewed by: Ştefan Mirică
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3536
OpenAlex ID: W2018895295
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DOI: 10.1006/JDEQ.1998.3536
author: Zvi Artstein
description: scientific article; zbMATH DE number 1283665