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Russian Academy of Sciences. Sbornik. Mathematics, 1994, Volume 77, Issue 1, Pages 213–230
DOI: https://doi.org/10.1070/SM1994v077n01ABEH003437
(Mi sm1081)
 

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

On the theory of the matrix Riccati equation. II

M. I. Zelikin
References:
Abstract: This paper is a continuation of the author's previous paper [1] with the same title, which contains an investigation of properties of the matrix Riccati equation with variable coefficients that arises from variational problems. For the investigation the matrix cross-ratio was introduced – an invariant of a quadruple of points in the Grassmann manifold of $n$-dimensional subspaces in a $2n$-dimensional linear space with respect to the action of the unimodular group of generalized linear fractional transformations on the Grassmann manifold. The properties of the matrix cross-ratio are investigated in the present article; classes of complex Riccati equations giving rise to flows on homogeneous Siegel domains of types I, II, and III are distinguished; a matrix analogue of the Schwarzian derivative is introduced.
Received: 10.07.1991
Bibliographic databases:
UDC: 517.977
MSC: Primary 34G20; Secondary 15A22
Language: English
Original paper language: Russian
Citation: M. I. Zelikin, “On the theory of the matrix Riccati equation. II”, Russian Acad. Sci. Sb. Math., 77:1 (1994), 213–230
Citation in format AMSBIB
\Bibitem{Zel92}
\by M.~I.~Zelikin
\paper On the theory of the~matrix Riccati equation.~II
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 1
\pages 213--230
\mathnet{http://mi.mathnet.ru//eng/sm1081}
\crossref{https://doi.org/10.1070/SM1994v077n01ABEH003437}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1202793}
\zmath{https://zbmath.org/?q=an:0786.49023}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1994SbMat..77..213Z}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994MZ10900013}
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  • https://doi.org/10.1070/SM1994v077n01ABEH003437
  • https://www.mathnet.ru/eng/sm/v183/i10/p87
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    This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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