Invariant Algebraic Surfaces and Impasses

Author(s)

da Silva, Paulo Ricardo ^[1] ; Perez, Otavio Henrique ^[1]

Affiliation

^[1] Sao Paulo State Univ Unesp, Inst Biosci Human & Exact Sci, Rua C Colombo 2265, BR-15054000 Sao Paulo - Brazil

• Document type: Journal article
• Source: Qualitative Theory of Dynamical Systems; v. 20, n. 2 JUL 2021.
• Web of Science Citations: 0

Abstract

Polynomial vector fields X : R-3 -> R-3 that have invariant algebraic surfaces of the form M = [f (x,y)z - g(x,y) = 0] are considered. We prove that trajectories of X on M are solutions of a constrained differential system having I = [f (x, y) = 0) as impasse curve. The main goal of the paper is to study the flow on M near points that are projected on typical impasse singularities. The Falkner-Skan equation (Llibre and Valls in Comput Fluids 86:71-76,2013), the Lorenz system (Llibre and Zhang in J Math Phys 43:1622-1645,2002) and the Chen system (Lu and Zhang in Int J Bifurc Chaos 17-8:2739-2748,2007) are some of the well-known polynomial systems that fit our hypotheses. (AU)

• FAPESP's process: 16/22310-0 - Discontinuous foliations and impasses
• Grantee: Otavio Henrique Perez
• Support Opportunities: Scholarships in Brazil - Doctorate