Invariant Algebraic Surfaces and Impasses

Autor(es)

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

Afiliação do(s) autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: Qualitative Theory of Dynamical Systems; v. 20, n. 2 JUL 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 16/22310-0 - Folheações descontínuas e impasses
• Beneficiário: Otavio Henrique Perez
• Modalidade de apoio: Bolsas no Brasil - Doutorado