Linear Symplectic Dynamic Systems

Martin Bohner and Allan Peterson
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Martin Bohner: Univeristy of Missouri-Rolla, Department of Mathematics
Allan Peterson: University of Nebraska, Department of Mathematics

Chapter Chapter 7 in Dynamic Equations on Time Scales, 2001, pp 289-314 from Springer

Abstract: Abstract In this chapter we investigate so-called symplectic systems of dynamic equations, which have a variety of important equations as their special cases, e.g., linear Hamiltonian dynamic systems or Sturm-Liouville dynamic equations of higher (even) order. Many of the results in this chapter can be found in DošlÝ and Hilscher [121], and are extensions of results by Bohner and DošlÝ [76]. Throughout this chapter we denote by $$ \mathcal{J} $$ the 2n × 2n-matrix $$ \mathcal{J} = \left( {\begin{array}{*{20}c} 0 & I \\ { - I} & 0 \\ \end{array} } \right). $$ We start by recalling the concepts of symplectic and Hamiltonian matrices.

Date: 2001
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DOI: 10.1007/978-1-4612-0201-1_7

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