Gradient systems of harmonic polynomials

[摘要] We characterize all local phase-portraits of the finite and infinite singular points of the gradient systems defined by the real harmonic polynomials in two variables. We classify all the non-equivalent topological phase portraits of the gradient systems in the Poincare disc defined by harmonic polynomials of degree less than five. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-11-15

[关键词] Harmonic polynomial;Gradient system;Phase portrait