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Sbornik: Mathematics, 2008, Volume 199, Issue 10, Pages 1505–1521
DOI: https://doi.org/10.1070/SM2008v199n10ABEH003970 (Mi sm4503) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Multidimensional versions of Poincaré's theorem for difference equations

E. K. Leinartasa, M. Passareb, A. K. Tsikha

a Siberian Federal University
b Stockholm University
English version PDF (388 kB) Citations (14)
References:
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DOI: https://doi.org/10.1070/SM2008v199n10ABEH003970
Abstract: A generalization to several variables of the classical Poincaré theorem on the asymptotic behaviour of solutions of a linear difference equation is presented. Two versions are considered: 1) general solutions of a system of $n$ equations with respect to a function of $n$ variables and 2) special solutions of a scalar equation. The classical Poincaré theorem presumes that all the zeros of the limiting symbol have different absolute values. Using the notion of an amoeba of an algebraic hypersurface, a multidimensional analogue of this property is formulated; it ensures nice asymptotic behaviour of special solutions of the corresponding difference equation.
Bibliography: 20 titles.
Received: 27.12.2007
Russian version:
Matematicheskii Sbornik, 2008, Volume 199, Number 10, Pages 87–104
DOI: https://doi.org/10.4213/sm4503
Bibliographic databases:
UDC: 517.55+517.965
MSC: Primary 39A11; Secondary 32A60
Language: English
Original paper language: Russian
Citation: E. K. Leinartas, M. Passare, A. K. Tsikh, “Multidimensional versions of Poincaré's theorem for difference equations”, Mat. Sb., 199:10 (2008), 87–104; Sb. Math., 199:10 (2008), 1505–1521
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v199/i10/p87
    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:78
    First page:26
     
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