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Matematicheskie Zametki, 2007, Volume 82, Issue 5, Pages 678–689
DOI: https://doi.org/10.4213/mzm4082 (Mi mzm4082) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Convergence of the Krylov–Bogolyubov Procedure in Bowan's Example

T. I. Golenishcheva-Kutuzovaa, V. A. Kleptsynb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Institute of Mathematical Research of Rennes
Full-text PDF (521 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm4082
Abstract: In this paper, we study the behavior of time averages of a measure in Bowan's example: a vector field on the plane with two saddles joined by two separatrix connections. We present an explicit criterion for the convergence of averaged measures and describe the set of their partial limits. As a consequence, we show that, for a typical initial measure, its time averages do not converge.
Keywords: vector field in the plane, invariant measure, time average of a measure, Poincaré map, Krylov–Bogolyubov procedure, Bowan's example.
Received: 15.05.2006
English version:
Mathematical Notes, 2007, Volume 82, Issue 5, Pages 608–618
DOI: https://doi.org/10.1134/S0001434607110041
Bibliographic databases:
UDC: 517.938
Language: Russian
Citation: T. I. Golenishcheva-Kutuzova, V. A. Kleptsyn, “Convergence of the Krylov–Bogolyubov Procedure in Bowan's Example”, Mat. Zametki, 82:5 (2007), 678–689; Math. Notes, 82:5 (2007), 608–618
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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