Publication details

Trigonometric and hyperbolic systems on time scales

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
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.
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