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Motivation and Preliminaries

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Symplectic Difference Systems: Oscillation and Spectral Theory

Part of the book series: Pathways in Mathematics ((PATHMATH))

Abstract

In this chapter we describe main motivating factors for the investigation of symplectic difference systems in this book. This motivation comes from several sources, mainly from (i) a generalization of the theory of second-order Sturm-Liouville difference equations, (ii) discrete variational analysis, (iii) (classical and discrete) Hamiltonian mechanics, (iv) discrete analogy of the theory of linear Hamiltonian differential systems, and (v) numerical methods for Hamiltonian differential systems preserving the symplectic structure.

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Authors and Affiliations

  1. Department of Mathematics and Statistics Faculty of Science, Masaryk University, Brno, Czech Republic

    Ondřej Došlý & Roman Šimon Hilscher

  2. Department of Applied Mathematics, Moscow State Technological University “STANKIN”, Moscow, Russia

    Julia Elyseeva

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  1. Ondřej Došlý
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Došlý, O., Elyseeva, J., Hilscher, R.Š. (2019). Motivation and Preliminaries. In: Symplectic Difference Systems: Oscillation and Spectral Theory. Pathways in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-19373-7_1

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