The stability of linear periodic Hamiltonian systems on time scales (Q1931244)

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.