Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves. Issue 3 (3rd July 2017)

• Record Type: Journal Article
• Authors: Llibre, Jaume; Messias, Marcelo; Reinol, Alisson C.
• Is Part Of: Dynamical systems. Volume 32:Issue 3(2017)
• Page Start: 374
• Page End: 390
• Publication Date: 2017-07-03
• Subjects: Quadratic and cubic vector fields -- invariant algebraic curves -- limit cycles -- Poincaré compactification -- global analysis -- normal forms; 34C05 -- 34C07 -- 34C08 -- 34C20 -- 34C25 -- 37G10; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2016.1263600
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C 1 and C 2 as invariant algebraic curves and the function, with α and β real values, as first integral. Moreover, we classify all global phase portraits on the Poincaré disc of a subclass of these vector fields.