New results for time reversed symplectic dynamic systems and quadratic functionals

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Authors	ŠIMON HILSCHER Roman ZEMÁNEK Petr
Year of publication	2012
Type	Article in Periodical
Magazine / Source	Electronic Journal of Qualitative Theory of Differential Equations
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Time scale; Symplectic system; Linear Hamiltonian system; Quadratic functional; Jacobi system; Reid roundabout theorem
Attached files	ejqtde_trssts_online_copy.pdf
Description	In this paper, we examine time scale symplectic (or Hamiltonian) systems and the associated quadratic functionals which contain a forward shift in the time variable. Such systems and functionals have a close connection to Jacobi systems for calculus of variations and optimal control problems on time scales. Our results, among which we consider the Reid roundabout theorem, generalize the corresponding classical theory for time reversed discrete symplectic systems, as well as they complete the recently developed theory of time scale symplectic systems.
Related projects:	Mathematical structures and their physical applications Diferenční rovnice a dynamické rovnice na time scales III