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A perturbation theorem for linear Hamiltonian systems with bounded orbits

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  • This paper concerns the Sacker-Sell spectral decomposition of a one-parametric perturbation of a non-autonomous linear Hamiltonian system with bounded solutions. Conditions ensuring the continuous variation with respect to the parameter of the spectral intervals and subbundles are established. These conditions depend on the perturbation direction and are closely related to the topological structure of the flows induced by the initial system on the real and complex Lagrange bundles.
    Mathematics Subject Classification: Primary 37B55, 34D08; Secondary 34C11, 37D20.


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