Browsing by Author "Magalhaes, Luis"
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Item The Asymptotics of Solutions of Singularly Perturbed Functional Differential Equations: and Concentrated Delays are Different(1983) Magalhaes, LuisThis paper illustrated the differences between systems with distributed delays and systems having only concentrated delays in what concerns the asymptotic rates of solutions of singularly perturbed linear retarded functional differential equations. An example of a system with distributed delays shows that the introduction of a ``slow" variable coupled with the ``fast" variable may decrease the asymptotic rates of solutions observed when the perturbation parameter is close to zero. Such a situation cannot happen for ordinary differential equations, or even for differential-difference equations.Item Invariant Manifolds for Functional Differential Equations Close to Ordinary Differential Equations(1983) Magalhaes, LuisThis paper considers invariant manifolds of global trajectories of retarded Functional Differential Equations in Rn. The persistence, smoothness and stability of such manifolds where the flow is given by an Ordinary Differential Equation (ODE) in Rn is studied for small perturbations of ODEs. The novelty of the present approach lies in the use of the dynamics of the flow on the manifolds, instead of their attractivity properties.Item Manifolds of Global Solutions of Functional Differential Equations(1983) Magalhaes, LuisThis paper consider smooth invariant manifolds of global solutions of retarded Functional Differential Equations in Rn. The persistence, under small perturbations, of such manifolds where the flow is given by an Ordinary Differential Equation in Rn is studied. The novelty of the present approach lies on the use of the dynamics of the flow on the manifolds, instead of their attractivity properties.Item