On linear systems with quasiperiodic coefficients and bounded solutions

  • V. I. Tkachenko

Abstract

For a discrete dynamical system ω n 0n, 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=A0n)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.
Published
25.01.1996
How to Cite
TkachenkoV. I. “On Linear Systems With Quasiperiodic Coefficients and Bounded Solutions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 48, no. 1, Jan. 1996, pp. 109-15, https://umj.imath.kiev.ua/index.php/umj/article/view/5368.
Section
Research articles