Title

Hamiltonian Systems on Time Scales

Abstract

Linear and nonlinear Hamiltonian systems are studied on time scales . We unify symplectic flow properties of discrete and continuous Hamiltonian systems. A chain rule which unifies discrete and continuous settings is presented for our so-called alpha derivatives on generalized time scales. This chain rule allows transformation of linear Hamiltonian systems on time scales under simultaneous change of independent and dependent variables, thus extending the change of dependent variables recently obtained by Došlý and Hilscher. We also give the Legendre transformation for nonlinear Euler–Lagrange equations on time scales to Hamiltonian systems on time scales.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Hamiltonian systems; time scales; Euler-Lagrange equations; delta derivatives; alpha derivatives; chain rule; Symplectic flows

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2000 Elsevier, All rights reserved.


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