2003
DOI: 10.1023/b:nono.0000016415.37855.86
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On the Existence of a Smooth Bounded Semiinvariant Manifold for a Degenerate Nonlinear System of Difference Equations in the Space m

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Cited by 2 publications
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“…In [3][4][5][6], this method was used for the investigation of invariant tori of countable systems of ordinary differential equations defined on tori. In the last ten years, several works were published (see [7][8][9][10][11][12][13][14][15]) in which this method was used for the investigation of invariant tori of countable systems of difference-differential and difference equations. In the present paper, in the space of bounded number sequences, we pose and solve the problem of finding sufficient conditions for the existence of invariant tori for linear and quasilinear countable systems of difference-differential equations defined on infinite-dimensional tori and containing an infinite set of constant different-sign deviations of a scalar argument.…”
Section: Statement Of the Problemmentioning
confidence: 99%
“…In [3][4][5][6], this method was used for the investigation of invariant tori of countable systems of ordinary differential equations defined on tori. In the last ten years, several works were published (see [7][8][9][10][11][12][13][14][15]) in which this method was used for the investigation of invariant tori of countable systems of difference-differential and difference equations. In the present paper, in the space of bounded number sequences, we pose and solve the problem of finding sufficient conditions for the existence of invariant tori for linear and quasilinear countable systems of difference-differential equations defined on infinite-dimensional tori and containing an infinite set of constant different-sign deviations of a scalar argument.…”
Section: Statement Of the Problemmentioning
confidence: 99%