Stability Zones for Discrete Time Hamiltonian Systems

Vladimir Rasvan

Address. Dept. of Automatic Control, Faculty of Autom., Comp. and Electr., Craiova University, A.I. Cuza str. No. 13,                         RO-1100, Craiova, Romania


Abstract. The discrete version of the Hamiltonian system $$ \dot{x}=\lambda JH(t)x $$ with $H(t)=H^*(t)=H(t+T)$ is considered. Following the line of M.G. Krein the stability zones with respect to the parameter $\lambda$ are considered: the side zones have to be estimated from multiplier traffic rules while the central stability zone from the discrete version of the skew - periodic boundary value problem.

AMSclassification. 39A10, 39A11, 39A12

Keywords. Discrete Hamiltonians, strong stability, $\lambda$-zones