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Perturbations of Jordan Difference Systems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2129)

Abstract

In this brief chapter, we only consider perturbations of systems of difference equations with a single non-singular Jordan block. That is, we consider

$$\displaystyle{ y(n+1) = \left [\lambda I + N + R(n)\right ]y(n),\qquad \lambda \neq 0,\qquad N = \left (\begin{array}{cccc} 0&1&& \\ &0 &\ddots & \\ & &\ddots&1\\ & & &0 \end{array} \right )\,,\qquad n \geq n_{0}. }$$
(7.1)

Following the approach taken in Sect. 6.2, the next theorem can be considered as a discrete counterpart of Corollary 6.2, and its proof is parallel to the proof given in Theorem 6.1.

Keywords

  • Discrete Counterpart
  • Jordan Block
  • Difference Equations
  • Elaydi
  • Perturba

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. S. Elaydi, An extension of Levinson’s theorem to asymptotically Jordan difference equations. J. Differ. Equ. Appl. 1, 369–390 (1995)

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  2. S. Elaydi, Asymptotics for linear difference equations I: basic theory. J. Differ. Equ. Appl. 5, 563–589 (1999)

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Bodine, S., Lutz, D.A. (2015). Perturbations of Jordan Difference Systems. In: Asymptotic Integration of Differential and Difference Equations. Lecture Notes in Mathematics, vol 2129. Springer, Cham. https://doi.org/10.1007/978-3-319-18248-3_7

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