Invariant measures of differential inclusions applied to singular perturbations
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: \((x',\varepsilon y')\in G(x,y)\).
scientific article; zbMATH DE number 1283665
scientific article