Trigonometric and hyperbolic systems on time scales

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Authors	ŠIMON HILSCHER Roman ZEMÁNEK Petr
Year of publication	2009
Type	Article in Periodical
Magazine / Source	Dynamic Systems and Applications
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Time scale; Time scale symplectic system; Linear Hamiltonian system; Discrete symplectic system; Trigonometric system; Hyperbolic system; Trigonometric function; Hyperbolic function
Attached files	Trigonometric_and_hyperbolic_systems_on_time_scales__Hilscher___Zemanek_.pdf
Description	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.
Related projects:	Mathematical structures and their physical applications Asymptotika, oscilace a kvadratické funkcionály v teorii dynamických rovnic Difference equations and dynamic equations on time scales II