On the existence of an integral invariant of a smooth dynamic system
type: Item
instance of: scholarly article
title: On the existence of an integral invariant of a smooth dynamic system
zbMATH Open document ID: 0664.70018
DOI: 10.1016/0021-8928(87)90078-5
published in: Journal of Applied Mathematics and Mechanics
publication date: 1987-01-01T00:00:00Z
review text: The existence of an integral invariant with a smooth density for a dynamic system in a cylindrical phase space is considered. The well-known Krylov-Bogolyubov theorem guarantees the existence of an invariant measure for any system in a compact space. But this measure is often concentrated in invariant sets of small dimensionality and in general is not an integral invariant with a summable density. For useful applications of ergodic theory, and in the theory of the Euler-Jacobi integrating factor, an invariant measure in the form of an integral invariant with smooth density is useful. Effective criteria for the existence of such measures in smooth dynamic systems are described. The general results are illustrated by examples from non-holonomic mechanics.
Mathematics Subject Classification ID: 70F25
Mathematics Subject Classification ID: 70G10
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 4087105
zbMATH Keywords: existence of an integral invariant
zbMATH Keywords: cylindrical phase space
zbMATH Keywords: Krylov- Bogolyubov theorem
zbMATH Keywords: invariant measure
zbMATH Keywords: ergodic theory
zbMATH Keywords: Euler-Jacobi integrating factor
zbMATH Keywords: non-holonomic mechanics
author: Valery V. Kozlov
MaRDI profile type: Publication
full work available at URL: 0021-8928(87)90078-5
OpenAlex ID: W1993330078
cites work: Q3264374
cites work: Q3234755
cites work: On realizing nonholonomic constraints by viscous friction forces and Celtic stones stability
description: scientific article; zbMATH DE number 4087105