Dynamics in Infinite Dimensions

By Jack K. Hale, L. Magalhães, W. M. Oliva. 2002

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Spectral convergence and nonlinear dynamics of reaction–diffusion equations under perturbations of the domain (2004, background): “Notice that, if moreover we assume the transversality of the stable and unstable manifolds in A0 then for e small enough the flow in the attractor Ae is Cconjugate with the flow in A0; in the sense that there exist homeomorphisms he : Ae-A0 such that for all ueAAe; we have TeðtÞðueÞ 1⁄4 h 1 e T0ðtÞh”
Generic Morse-Smale property for the parabolic equation on the circle (2010, background): “Oliva [40] (see also [20]) has proved that the Morse–Smale dynamical systems S(t), generated by “dissipative” parabolic equations or more generally by “dissipative in finite time smoothing equations”, are structurally stable, in the sense that the restrictions of the flows to the compact global attr”
Bifurcations and multiple traffic jams in a car-following model with reaction-time delay (2005, background): “The velocity of the i-th vehicle is denoted vi and its distance to the preceding i + 1-th vehicle, known as the headway, is denoted by hi.”
Dynamics and Control at Feedback Vertex Sets. I: Informative and Determining Nodes in Regulatory Networks (2013, background): “Meanwhile this concept has attracted a lot of attention; see for example the monographs [4,8,10,14,16,22,32,33,36] and the references there.”