Abstract
Already in an analysis of nonlinear systems, linear problems frequently occur in form of variational equations (cf. Corollary 2.3.11) when linearizing along a given reference solution. Provided this solution does lack a specific time-dependence (e.g., (almost) periodicity, or being convergent), then the resulting variational equations are nonautonomous in the general sense. A further reason for the importance of linear equations is that the difference of two solutions to a nonlinear problem always solves a linear homogeneous difference equation, as follows from an easy application of the mean value theorem (cf. [295, p. 341, Theorem 4.2]). Finally, a solid linear theory opens the door to utilize appropriate perturbation results and to generalize a global geometric theory to semilinear equations. In this chapter, we present the corresponding theory.
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Pötzsche, C. (2010). Linear Difference Equations. In: Geometric Theory of Discrete Nonautonomous Dynamical Systems. Lecture Notes in Mathematics(), vol 2002. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14258-1_3
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DOI: https://doi.org/10.1007/978-3-642-14258-1_3
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14257-4
Online ISBN: 978-3-642-14258-1
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