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One subfamily of cubic systems with invariant lines of total multiplicity eight and with two distinct real infinite singularities
Authors: Bujac Cristina
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Abstract
In this article we classify a subfamily of differential real cubic systems possessing eight invariant straight lines, including the line at infinity and including their multiplicities. This subfamily of systems is characterized by the existence of two distinct infinite singularities, defined by the linear factors of the polynomial\ $ C_3(x,y)=yp_3(x,y)-xq_3(x,y)$,\ where $p_3$ and $q_3$ are the cubic homogeneities of these systems. Moreover we impose additional conditions related with the existence of triplets and/or couples of parallel invariant lines. 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.Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
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Academy of Sciences of Moldova
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Fulltext
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Contents
- On fixed point subalgebras of some local algebras over a field
- Stability radius bounds in multicriteria Markowitz portfolio problem with venturesome investor criteria
- lp(R)-equivalence of topological spaces and topological modules
- One subfamily of cubic systems with invariant lines of total multiplicity eight and with two distinct real infinite singularities
- Primary decomposition of general graded structures
- On the distinction between one-dimensional Euclidean and hyperbolic spaces
- On the number of ring topologies on countable rings
- Determining the Optimal Evolution Time for Markov Processes with Final Sequence of States
