Trigonometric and hyperbolic systems on time scales
Roman Šimon Hilscher, Petr Zemánek · Dynamic Systems and Applications · 2009
In this paper we discuss trigonometric and hyperbolic systems on time scales. These systems generalize and unify their corresponding continuous-time and discrete-time analo- gies, 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 calcu- lus extend to this general setting, including the time scale differentiation of these functions. AMS (MOS) Subject Classification. 34C99, 39A12