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Mat. Sb., 2008, Volume 199, Number 5, Pages 35–44 (Mi msb4504)  

This article is cited in 2 scientific papers (total in 2 papers)

A sufficient condition for reduction by stages: proof and applications

I. V. Mykytyukab, A. M. Stepincd

a Institute of Mathematics, Rzeszów University
b Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS Ukraine
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
d Russian State University for the Humanities

Abstract: In this paper we prove the Marsden-Misiołek-Ortega-Perlmutter-Ratiu Stages Hypothesis, which is a sufficient condition for a general reduction by stages theorem. Our Lie-algebraic approach allows us to prove this conjecture in a general case (not only for semidirect products of groups with cocycle) and to simplify the proof of a general reduction by stages theorem (with some modifications).
Bibliography: 8 titles.

DOI: https://doi.org/10.4213/sm4504

Full text: PDF file (456 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2008, 199:5, 663–671

Bibliographic databases:

UDC: 514.756.4
MSC: 37J15, 53D20
Received: 30.12.2007

Citation: I. V. Mykytyuk, A. M. Stepin, “A sufficient condition for reduction by stages: proof and applications”, Mat. Sb., 199:5 (2008), 35–44; Sb. Math., 199:5 (2008), 663–671

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb4504
  • https://doi.org/10.4213/sm4504
  • http://mi.mathnet.ru/eng/msb/v199/i5/p35

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bavo Langerock, Tom Mestdag, Joris Vankerschaver, “Routh Reduction by Stages”, SIGMA, 7 (2011), 109, 31 pp.  mathnet  crossref
    2. Mykytyuk I.V., “Structure of the coadjoint orbits of Lie algebras”, J. Lie Theory, 22:1 (2012), 251–268  mathscinet  zmath  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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