Conţinutul numărului revistei |
Articolul precedent |
Articolul urmator |
223 0 |
SM ISO690:2012 BUJAC, Cristina, VULPE, Nicolae. Cubic Systems with Invariant Straight Lines of Total Multiplicity Eight and with Three Distinct Infinite Singularities. In: Qualitative Theory of Dynamical Systems, 2015, vol. 14, pp. 109-137. ISSN 1575-5460. DOI: https://doi.org/10.1007/s12346-014-0126-8 |
EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
Qualitative Theory of Dynamical Systems | ||||||
Volumul 14 / 2015 / ISSN 1575-5460 /ISSNe 1662-3592 | ||||||
|
||||||
DOI:https://doi.org/10.1007/s12346-014-0126-8 | ||||||
Pag. 109-137 | ||||||
|
||||||
Rezumat | ||||||
In this article we prove a classification theorem (Main Theorem) of real planar cubic vector fields which possess eight invariant straight lines, including the line at infinity and including their multiplicities and in addition they possess three distinct infinite singularities. This classification, which is taken modulo the action of the group of real affine transformations and time rescaling, is given in terms of affine invariant polynomials. The invariant polynomials allow one to verify for any given real cubic system whether or not it has invariant straight lines of total multiplicity eight, and to specify its configuration of straight lines endowed with their corresponding real singularities of this system. The calculations can be implemented on computer and the results can therefore be applied for any family of cubic systems in this class, given in any normal form. |
||||||
Cuvinte-cheie affine invariant polynomial, algebraic invariant curve, configuration of invariant straight lines, Cubic differential system, Group action, multiplicity of an invariant straight line, Poincare compactification, singular points |
||||||
|