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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 163, Number 1, Pages 45–78
DOI: https://doi.org/10.4213/tmf6486
(Mi tmf6486)
 

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

Complanart of a system of polynomial equations

A. D. Vlasov

Institute for Theoretical and Experimental Physics, Moscow, Russia
Full-text PDF (687 kB) Citations (1)
References:
Abstract: We study homogeneous polynomial maps of vector spaces $z_i\to A_i^{i_1i_2\dots i_s}z_{i_1}z_{i_2}\cdots z_{i_s}$ and their eigenvectors and eigenvalues. We define a new quantity called the complanart, which determines the coplanarity of the solution vectors of a system of polynomial equations. Evaluating the complanart reduces to evaluating resultants. As in the linear case, the pattern of eigenvectors/eigenvalues defines the phase diagram of the associated differential equation. Such differential equations arise naturally in attempting to extend Lyapunov's stability theory. The results in this paper can be used in a range of applications from solving nonlinear differential equations and calculating nonlinear exponents to evaluating non-Gaussian integrals.
Keywords: resultant, complanart, nonlinear eigenvector, nonlinear differential equation.
Received: 03.08.2009
English version:
Theoretical and Mathematical Physics, 2010, Volume 163, Issue 1, Pages 438–465
DOI: https://doi.org/10.1007/s11232-010-0034-2
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. D. Vlasov, “Complanart of a system of polynomial equations”, TMF, 163:1 (2010), 45–78; Theoret. and Math. Phys., 163:1 (2010), 438–465
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6486
  • https://doi.org/10.4213/tmf6486
  • https://www.mathnet.ru/eng/tmf/v163/i1/p45
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:479
    Full-text PDF :238
    References:63
    First page:18
     
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