Convergence of the Krylov-Bogolyubov procedure in Bowan's example
type: Item
instance of: scholarly article
title: Convergence of the Krylov-Bogolyubov procedure in Bowan's example
zbMATH Open document ID: 1149.37013
DOI: 10.1134/S0001434607110041
author: Tatiana Golenishcheva-Kutuzova
author: Victor Kleptsyn
published in: Mathematical Notes
publication date: 2008-09-02T00:00:00Z
review text: A vector field on the plane is studied with two saddles jointed by two separatrix connections. This is the so called Bowan's example and more precisely the authors investigate the behaviour of time averages of the measure. They prove a necessary and sufficient condition on the measure for which there is a limit in the Krylov-Bogolyubov procedure. In the case of no limit, the set of partial limits is derived.
reviewed by: Angela Slavova
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37C40
zbMATH DE Number: 5319707
zbMATH Keywords: vector field in the plane
zbMATH Keywords: invariant measure
zbMATH Keywords: time average of a meassure
zbMATH Keywords: Poincare map
zbMATH Keywords: Krilov-Bogolyubov procedure
zbMATH Keywords: Bowan's example
MaRDI profile type: Publication
cites work: Time Averages for Heteroclinic Attractors
cites work: Heteroclinic attractors: Time averages and moduli of topological conjugacy
cites work: Asymptotic measures and distributions of Birkhoff averages with respect to Lebesgue measure
cites work: GIBBS MEASURES IN ERGODIC THEORY
cites work: A Measure Associated with Axiom-A Attractors
cites work: Equilibrium states and the ergodic theory of Anosov diffeomorphisms
cites work: Multicomponent dynamical systems: SRB measures and phase transitions
cites work: Q5711907
cites work: Relations between natural and observable measures
cites work: What are SRB measures, and which dynamical systems have them?
cites work: Q3701686
cites work: An example of non-coincidence of minimal and statistical attractors
full work available at URL: s0001434607110041
OpenAlex ID: W2070488364
description: scientific article; zbMATH DE number 5319707