| Title: | Rational involutions and an application to planar systems of ODE |
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| Authors: | ID Mastev, Ivan (Author)
ID Romanovski, Valery (Author)
ID Tian, Yun (Author) |
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| Files: |  mathematics-12-00486-v3.pdf (3,25 MB)
MD5: B0F3FBB883757A0AA29DFFD8F2C29C39
 https://www.mdpi.com/2227-7390/12/3/486
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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
FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | An involution refers to a function that acts as its own inverse. In this paper, our focus lies on exploring two-dimensional involutive maps defined by rational functions. These functions have denominators represented by polynomials of degree one and numerators by polynomials of a degree of, at most, two, depending on parameters. We identify the sets in the parameter space of the maps that correspond to involutions. The investigation relies on leveraging algorithms from computational commutative algebra based on the Groebner basis theory. To expedite the computations, we employ modular arithmetic. Furthermore, we showcase how involution can serve as a valuable tool for identifying reversible and integrable systems within families of planar polynomial ordinary differential equations. |
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| Keywords: | involutions, reversibility, integrability, centers, cubic systems |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 09.01.2024 |
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| Article acceptance date: | 29.01.2024 |
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| Publication date: | 02.02.2024 |
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| Publisher: | MDPI |
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| Year of publishing: | 2024 |
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| Number of pages: | 16 str. |
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| Numbering: | let. 12, št. 3, št. članka 486 |
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| PID: | 20.500.12556/DKUM-89790  |
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| UDC: | 51 |
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| ISSN on article: | 2227-7390 |
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| COBISS.SI-ID: | 184531971 |
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| DOI: | 10.3390/math12030486 |
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| Copyright: | © 2024 by the authors |
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| Publication date in DKUM: | 12.08.2024 |
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| Views: | 213 |
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| Downloads: | 92 |
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| Metadata: |    |
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| Categories: | Misc.
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