20.500.12556/DKUM-89790 Rational involutions and an application to planar systems of ODE 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. involutions reversibility integrability centers cubic systems involucijsko reverzibilnost integrabilnost true false true MDPI Angleški jezik Slovenski jezik https://www.mdpi.com/journal/mathematics © 2024 by the authors Članek v reviji 2024-08-12 12:27:57 2024-08-12 12:27:58 2025-07-03 08:31:37 0000-00-00 00:00:00 2024 0 0 16 str. št. 3, št. članka 486 let. 12 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2024-01-09 2024-01-29 2024-02-02 51 184531971 10.3390/math12030486 2227-7390 mathematics-12-00486-v3.pdf mathematics-12-00486-v3.pdf 1 B0F3FBB883757A0AA29DFFD8F2C29C39 475c553c3d01ebaafec96d957baecd675178400346dddb960870a5849596e47f eb9e7c04-5895-11ef-a285-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=182267 https://www.mdpi.com/2227-7390/12/3/486 0 5ef2fc98-57d7-11f0-95d1-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=193199 Fakulteta za elektrotehniko, računalništvo in informatiko Fakulteta za naravoslovje in matematiko 0 0 0