Rational Involutions and an Application to Planar Systems of ODE

Ivan Mastev, Valery G. Romanovski () and Yun Tian
Additional contact information
Ivan Mastev: Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia
Valery G. Romanovski: Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia
Yun Tian: Department of Mathematics, Shanghai Normal University, 100 Guilin Rd., Shanghai 200234, China

Mathematics, 2024, vol. 12, issue 3, 1-16

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.

Keywords: involutions; reversibility; integrability; centers; cubic systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/3/486/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/3/486/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:3:p:486-:d:1332409

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().