To the problem of complementability of a periodic frame to a periodic basis
We obtain sufficient conditions (and necessary conditions in the simplest case) of complementability of a periodic frame to a periodic basis for the Euclidean space in terms of monodromy matrices of some linear system of differential equations built by using this periodic frame. We consider the pro...
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| Published in: | Нелінійні коливання |
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| Date: | 2001 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2001
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/174762 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | To the problem of complementability of a periodic frame to a periodic basis / O.A. Burylko, A.A. Davydenko // Нелінійні коливання. — 2001. — Т. 4, № 3. — С. 458-470. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We obtain sufficient conditions (and necessary conditions in the simplest case) of complementability of a periodic frame to a periodic basis for the Euclidean space in terms of monodromy matrices of some linear system of differential equations built by using this periodic
frame. We consider the problem of complementability for introducing local coordinates in a
neighbourhood of a smooth m-dimensional invariant torus of a dynamic system in the Euclidean space R
n
if the dimensions satisfy the inequality m + 1 < n ≤ 2m.
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| ISSN: | 1562-3076 |