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dc.contributor.author |
Clelland, J.N. |
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dc.contributor.author |
Moseley, C.G. |
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dc.contributor.author |
Wilkens, G.R. |
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dc.date.accessioned |
2019-02-19T17:20:18Z |
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dc.date.available |
2019-02-19T17:20:18Z |
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dc.date.issued |
2009 |
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dc.identifier.citation |
Geometry of Control-Affine Systems / J.N. Clelland, C.G. Moseley, G.R. Wilkens // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 26 назв. — англ. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2000 Mathematics Subject Classification: 58A30; 53C17; 58A15; 53C10 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/149099 |
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dc.description.abstract |
Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X – i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X) = n, rank(F) = n–1, and when dim(X) = 3, rank(F) = 1. Unlike linear distributions, which are characterized by integer-valued invariants – namely, the rank and growth vector – when dim(X) ≤ 4, we find local invariants depending on arbitrary functions even for rank 1 point-affine distributions on manifolds of dimension 2. |
uk_UA |
dc.description.sponsorship |
This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”. This work was partially supported by NSF grant DMS-0908456. |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут математики НАН України |
uk_UA |
dc.relation.ispartof |
Symmetry, Integrability and Geometry: Methods and Applications |
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dc.title |
Geometry of Control-Affine Systems |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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