| Title: | First integrals and invariants of systems of ordinary differential equations |
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| Authors: | ID Grašič, Mateja (Author)
ID Jarrah, Abdul Salam (Author)
ID Romanovski, Valery (Author) |
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| Files: |  RAZ_Grasic_Mateja_2025.pdf (362,83 KB)
MD5: 31AEC5FD9BBEEC043B2291336B30890C
 https://doi.org/10.3390/math13213485
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
FERI - Faculty of Electrical Engineering and Computer Science
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| Abstract: | We investigate the interplay between monomial first integrals, polynomial invariants of certain group action, and the Poincaré-Dulac normal forms for autonomous systems of ordinary differential equations with a diagonal matrix of the linear part. Using tools from computational algebra, we develop an algorithmic approach for identifying generators of the algebras of monomial and polynomial first integrals, which works in the general case where the matrix of the linear part includes algebraic complex eigenvalues. Our method also provides a practical tool for exploring the algebraic structure of polynomial invariants and their relation to the Poincaré-Dulac normal forms of the underlying vector fields. |
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| Keywords: | first integrals, polynomial invariants, Poincaré-Dulac normal form, systems of ordinary differential equations |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 08.10.2025 |
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| Article acceptance date: | 22.10.2025 |
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| Publication date: | 01.11.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 17 str. |
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| Numbering: | Letn. 13, št. 21, št. članka 3485 |
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| PID: | 20.500.12556/DKUM-96049  |
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| UDC: | 517.913 |
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| ISSN on article: | 2227-7390 |
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| COBISS.SI-ID: | 258934531 |
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| DOI: | 10.3390/math13213485 |
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| Publication date in DKUM: | 27.11.2025 |
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| Views: | 165 |
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| Downloads: | 8 |
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| Metadata: |    |
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| Categories: | Misc.
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