Multidimensional versions of Poincare's theorem for difference equations


Тип публикации: статья из журнала

Год издания: 2008

Идентификатор DOI: 10.1070/SM2008v199n10ABEH003970

Аннотация: A generalization to several variables of the classical Poincare theorem on the asymptotic behaviour of solutions of alinear difference equation is presented. Two versions are considered: 1)general solutions of asystem of n equations with respect to afunction of n variables and 2)special solutions of ascalar equation. The classical Показать полностьюPoincare theorem presumes that all the zeros of the limiting symbol have different absolute values. Using the notion of an amoeba of an algebraic hypersurface, amultidimensional analogue of this property is formulated; it ensures nice asymptotic behaviour of special solutions of the corresponding difference equation. © 2008 Russian Academy of Sciences, (DoM) and London Mathematical Society, Turpion Ltd.

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Журнал: Sbornik Mathematics

Выпуск журнала: Vol. 199, Is. 10

Номера страниц: 1505-1521


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