Diego M. Benardete

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One-dimensional differential equations dy/dt = f (t, y) that are periodic in t arise in many areas of applied mathematics. The attracting and repelling periodic solutions and their bifurcations are the key qualitative features that determine the observed behavior of the system being modeled. One quickly finds that the low dimensional character of the(More)
Let F and r' be lattices, and (p and 4> one-parameter subgroups of the connected Lie groups G and G'. If one of the following conditions (a), (b), or (c) hold, Theorem A states that if the induced flows on the homogeneous spaces G/T and G'/Y' are topologically equivalent, then they are topologically equivalent by an affine map. (a) G and G' are(More)
A Wilson–Cowan system, which models the interaction between subpopulations of excitatory and inhibitory neurons, is studied for the case in which the inhibitory neurons are receiving external periodic input. If the feedback within the excitatory population is large enough, the response of the system to large amplitude, low frequency input is determined by(More)
We define the asymptotic homotopy of trajectories of flows on closed manifolds. These homotopy cycles take values in the 2-step nilpotent Lie group which is associated to the fundamental group by means of Malcev completion. The cycles are an asymptotic limit along the orbit of the product integral of a Lie algebra valued 1-form. Propositions 5.1-5.7 show(More)
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