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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

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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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