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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm4503https://doi.org/10.1070/SM2008v199n10ABEH003970 https://www.mathnet.ru/eng/sm/v199/i10/p87
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Abstract page: | 1025 | Russian version PDF: | 342 | English version PDF: | 47 | References: | 78 | First page: | 26 |
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