# TRIGONOMETRIC AND HYPERBOLIC SYSTEMS ON TIME SCALES

 Title TRIGONOMETRIC AND HYPERBOLIC SYSTEMS ON TIME SCALES Publication Type Journal Article Year of Publication 2009 Authors HILSCHER R., ZEMANEK P. Journal Dynamic Systems and Applications Volume 18 Start Page 483 Pagination 23 Date Published 2009 ISSN 1056-2176 AMS Subject Classification 34C99, 39A12 Abstract In this paper we discuss trigonometric and hyperbolic systems on time scales. These systems generalize and unify their corresponding continuous-time and discrete-time analogies, namely the systems known in the literature as trigonometric and hyperbolic linear Hamiltonian systems and discrete symplectic systems. We provide time scale matrix definitions of the usual trigonometric and hyperbolic functions and show that many identities known from the basic calculus extend to this general setting, including the time scale differentiation of these functions. PDF https://acadsol.eu/dsa/articles/18/34-DSA-180.pdf Refereed Designation Refereed