Abstract
For a discrete dynamical system ω n =ω0+αn, where a is a constant vector with rationally independent coordinates, on thes-dimensional torus Ω we consider the setL of its linear unitary extensionsx n+1=A(ω0+αn)x n , whereA (Ω) is a continuous function on the torus Ω with values in the space ofm-dimensional unitary matrices. It is proved that linear extensions whose solutions are not almost periodic form a set of the second category inL (representable as an intersection of countably many everywhere dense open subsets). A similar assertion is true for systems of linear differential equations with quasiperiodic skew-symmetric matrices.
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Tkachenko, V.I. On linear systems with quasiperiodic coefficients and bounded solutions. Ukr Math J 48, 122–129 (1996). https://doi.org/10.1007/BF02390989
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DOI: https://doi.org/10.1007/BF02390989