Про лінійні системи з квазіперіодичними коефіцієнтами та обмеженими розв'язками
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-dimen...
Saved in:
| Date: | 1996 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут математики НАН України
1996
|
| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/157555 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Про лінійні системи з квазіперіодичними коефіцієнтами та обмеженими розв'язками / В.І. Ткаченко // Український математичний журнал. — 1996. — Т. 48, № 1. — С. 109-115. — Бібліогр.: 10 назв. — укр. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
|---|