Hamiltonian systems on time scales

Linear and nonlinear Hamiltonian systems are studied on time scales T. We u nify symplectic flow properties of discrete and continuous Hamiltonian syst ems. A chain rule which unifies discrete and continuous settings is present ed for our so-called alpha derivatives on generalized time scales. This cha in rule allows transformation of linear Hamiltonian systems on time scales under simultaneous change of independent and dependent variables, thus exte nding the change of dependent variables recently obtained by Dosly and Hils cher. We also give the Legendre transformation for nonlinear Euler-Lagrange equations on time scales to Hamiltonian systems on time scales. (C) 2000 A cademic Press.