Invariant Algebraic Surfaces of Polynomial Vector Fields in Dimension Three
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DOI: 10.1007/s10884-021-10080-8
Abstract: We discuss criteria for the nonexistence, existence and computation of invariant algebraic surfaces for three-dimensional complex polynomial vector fields, thus transferring a classical problem of Poincaré from dimension two to dimension three. Such surfaces are… read more here.
Keywords: vector; algebraic surfaces; polynomial vector; dimension three ... See more keywords
A Geometric Investigation of the Invariant Algebraic Curves in Two Dimensional Lotka–Volterra Systems
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DOI: 10.1007/s11786-017-0311-7
Abstract: The aim of this work is to investigate the geometric behaviour of the invariant algebraic curves in two dimensional Lotka–Volterra systems, first classified by Moulin-Ollagnier. read more here.
Keywords: lotka volterra; two dimensional; curves two; algebraic curves ... See more keywords
Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves
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DOI: 10.1080/14689367.2016.1263600
Abstract: ABSTRACT In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C1 and C2 as invariant algebraic curves and the function ,… read more here.
Keywords: vector; circles invariant; nonconcentric circles; two nonconcentric ... See more keywords