Ukrainian Mathematical Journal

, Volume 48, Issue 1, pp 122–129 | Cite as

On linear systems with quasiperiodic coefficients and bounded solutions

  • V. I. Tkachenko
Article
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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.

Keywords

Dense Subset Linear Differential Equation Linear Extension Unitary Matrice Fundamental System 
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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • V. I. Tkachenko

There are no affiliations available

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