| Title: | Integrability of polynomial vector fields and a dual problem |
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| Authors: | ID Petek, Tatjana (Author)
ID Romanovski, Valery (Author) |
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| Files: |  s12346-026-01484-2.pdf (705,50 KB)
MD5: 96F7E1D084FDDE0298484532CD2CE922
 https://link.springer.com/article/10.1007/s12346-026-01484-2
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FERI - Faculty of Electrical Engineering and Computer Science
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| Abstract: | We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability variety in relation to the invariants of the associated Lie group. Our study extends to differential operators on affine algebraic varieties, highlighting the intrinsic connection between these operators and local analytic first integrals. To illustrate the duality, the case of quadratic vector fields is considered in detail. |
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| Keywords: | integrabilnost, polinomialni sistem, invariantno, polynomial system of ODEs, integrability, first order linear PDE, multigraded rings, invariants |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 10.02.2026 |
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| Article acceptance date: | 04.03.2026 |
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| Publication date: | 23.03.2026 |
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| Publisher: | Springer Nature |
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| Year of publishing: | 2026 |
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| Number of pages: | 36 str. |
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| Numbering: | Vol. 25, [article no.] 63 |
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| PID: | 20.500.12556/DKUM-98091  |
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| UDC: | 51 |
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| ISSN on article: | 1662-3592 |
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| COBISS.SI-ID: | 278060035 |
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| DOI: | 10.1007/s12346-026-01484-2 |
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| Copyright: | © The Author(s) 2026 |
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| Publication date in DKUM: | 15.05.2026 |
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| Views: | 237 |
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| Downloads: | 5 |
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| Metadata: |    |
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| Categories: | Misc.
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