Resumen de Invariant Algebraic Surfaces and Impasses

Paulo Ricardo da Silva, Otavio Henrique Perez

• 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.