Invariant Algebraic Surfaces and Impasses

• Autor(a) principal: da Silva, Paulo Ricardo [UNESP]
• Data de Publicação: 2021
• Outros Autores: Perez, Otavio Henrique [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/s12346-021-00465-x; http://hdl.handle.net/11449/206067
• topic: Differential-algebraic equations; Implicit ordinary differential equations; Invariant manifolds

Polynomial vector fields X: R3→ R3 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.