dc.contributor.author | CIUBOTARU, Stanislav | |
dc.contributor.author | CALIN, Iurie | |
dc.date.accessioned | 2020-11-02T15:22:31Z | |
dc.date.available | 2020-11-02T15:22:31Z | |
dc.date.issued | 2018 | |
dc.identifier.citation | CIUBOTARU, Stanislav, CALIN, Iurie. Minimal polynomial basis of GL (2, R )-comitants and of GL (2, R )-invariants of the planar system of differential equations with nonlinearities of the fourth degree. In: CAIM 2018: The 26th Conference on Applied and Industrial Mathematics: Book of Abstracts, Technical University of Moldova, September 20-23, 2018. Chişinău: Bons Offices, 2018, pp. 33-35. | en_US |
dc.identifier.uri | http://repository.utm.md/handle/5014/10999 | |
dc.description | Only Abstract | en_US |
dc.description.abstract | The theory of algebraic invariants and comitants for polynomial autonomous systems of differential equations has been developed by C. Sibirschi and his disciples. One of the important problems concerning this theory is the construction of minimal polynomial bases of the invariants and comitants of the mentioned systems, with respect to different subgroups of the affine group of the transformations of their phase planes, in particular with respect to the subgroup GL(2, R). Some important results in this direction are obtained by academician C. Sibirschi and N.Vulpe. We remark, that polynomial bases for different combinations of homogeneous polynomials Pmj (x 1 , x 2) (j = 1, 2, m = 0, 1, 2, 3) in system were considered by E. Gasinskaya-Kirnitskaya, Dang Dinh Bich, D. Boularas, M. Popa, V. Ciobanu, V. Danilyuk, E. Naidenova. We establishe a conjecture that the minimal polynomial basis of GL(2, R)-comitants (respectively, of GL(2, R)-invariants) of system (1) consists from 419 elements (respectively, 182 elements) which must be of the above 111 (respectively, 42) types. | en_US |
dc.language.iso | en | en_US |
dc.publisher | Bons Offices | en_US |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 United States | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/us/ | * |
dc.subject | systems of differential equations | en_US |
dc.subject | invariants | en_US |
dc.subject | comitants | en_US |
dc.subject | polynomials | en_US |
dc.title | Minimal polynomial basis of GL (2, R )-comitants and of GL (2, R )-invariants of the planar system of differential equations with nonlinearities of the fourth degree | en_US |
dc.type | Article | en_US |
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