SO(2,R)-invariant polynomials of a differential system which are involved in solving the stability problem of unperturbed motion in the case of a center and a focus
Vol 21 No 1 (2026), EXACT SCIENCES
Vol 21 No 1 (2026)

SO(2,R)-invariant polynomials of a differential system which are involved in solving the stability problem of unperturbed motion in the case of a center and a focus

EXACT SCIENCES
https://doi.org/10.36120/2587-3644.v21i1.98-116
Published July 23, 2026
Natalia Neagu
“Ion Creangă” State Pedagogical University of Chisinau, 5 Gh. Iablocikin st.; Institute of Mathematics and Computer Science, Moldova State University, Republic of Moldova
https://orcid.org/0000-0003-3944-3688
Mihail Popa
Institute of Mathematics and Computer Science, Moldova State University, Republic of Moldova
https://orcid.org/0000-0003-2721-1185

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Keywords

differential system
rotation group
Lie operator
invariants and comitants
focus quantities
stability of unperturbed motion.

How to Cite

Neagu, N., & Popa, M. (2026). SO(2,R)-invariant polynomials of a differential system which are involved in solving the stability problem of unperturbed motion in the case of a center and a focus. Acta Et Commentationes Exact and Natural Sciences, 21(1), 98-116. https://doi.org/10.36120/2587-3644.v21i1.98-116
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Abstract

We consider a two-dimensional polynomial differential system s(1,m₁,...,mₗ) (l<∞), for which the origin is a singular point of the second group (center or focus). Using the Lie operator of the linear representation of the rotation group SO(2,R) in the space of phase variables and coefficients of the system s(1,m₁,...,mₗ) (l<∞), an upper bound is determined for the number of functionally independent SO(2,R)-invariant polynomials involved in solving the stability problem of the unperturbed motion described by this system.

https://doi.org/10.36120/2587-3644.v21i1.98-116