The stability of linear periodic Hamiltonian systems on time scales
The author considers the planar Hamiltonian system \[ x^\Delta=\alpha(t)x^\sigma+\beta(t)u,\;\;u^\Delta=-\gamma(t)x^\sigma-\alpha(t)u \] on an arbitrary time scale \(\mathbb{T}\), where \(\alpha,\beta,\gamma:\mathbb{T}\rightarrow\mathbb{R}\) are rd-continuous, \(\sigma:\mathbb{T}\rightarrow\mathbb{T}\) is the forward jump operator, and \(x^\sigma:=x\circ\sigma\). They give a new stability criterion for planar periodic Hamiltonian systems. The results obtained not only unify the related continuous and discrete ones but also provide sharper stability criteria for the discrete case.
scientific article; zbMATH DE number 6130502