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Regul. Chaotic Dyn., 2017, Volume 22, Issue 7, Pages 840–850 (Mi rcd294)  

This article is cited in 1 scientific paper (total in 1 paper)

Global Properties of Kovalevskaya Exponents

Andrzej J. Maciejewskia, Maria Przybylskab

a Janusz Gil Institute of Astronomy, University of Zielona Góra, ul. Licealna 9, 65-417, Zielona Góra, Poland
b Institute of Physics, University of Zielona Góra, ul. Licealna 9, PL-65–417, Zielona Góra, Poland

Abstract: This paper contains a collection of properties of Kovalevskaya exponents which are eigenvalues of a linearization matrix of weighted homogeneous nonlinear systems along certain straight-line particular solutions. Relations in the form of linear combinations of Kovalevskaya exponents with nonnegative integers related to the presence of first integrals of the weighted homogeneous nonlinear systems have been known for a long time. As a new result other nonlinear relations between Kovalevskaya exponents calculated on all straight-line particular solutions are presented. They were obtained by an application of the Euler–Jacobi–Kronecker formula specified to an appropriate n-form in a certain weighted homogeneous projective space.

Keywords: Kovalevskaya – Painlevé analysis, integrability, quasi-homogeneous systems

Funding Agency Grant Number
National Science Centre (Narodowe Centrum Nauki) DEC-2013/09/B/ST1/04130
The work has been supported by grant No. DEC-2013/09/B/ST1/04130 of the National Science Center of Poland.


DOI: https://doi.org/10.1134/S1560354717070061

References: PDF file   HTML file

Bibliographic databases:

MSC: 37J30, 34M45, 32A27
Received: 17.08.2017
Accepted:22.11.2017
Language:

Citation: Andrzej J. Maciejewski, Maria Przybylska, “Global Properties of Kovalevskaya Exponents”, Regul. Chaotic Dyn., 22:7 (2017), 840–850

Citation in format AMSBIB
\Bibitem{MacPrz17}
\by Andrzej J. Maciejewski, Maria Przybylska
\paper Global Properties of Kovalevskaya Exponents
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 7
\pages 840--850
\mathnet{http://mi.mathnet.ru/rcd294}
\crossref{https://doi.org/10.1134/S1560354717070061}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000425980500006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042467621}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Kozlov, “Tensor invariants and integration of differential equations”, Russian Math. Surveys, 74:1 (2019), 111–140  mathnet  crossref  crossref  adsnasa  isi  elib
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