Numerical Analysis Seminars: Dynamical systems in trajectory space
20 May 2016 14:00 in CM107
In this general audience talk, we take an innocent ordinary differential equation in R3, and blow it up into an infinite-dimensional system. The phase space for the new system is a space of trajectories. Certain trajectories in this space embody the long-time behavior of the original system, those in the global attractor. In one approach these distinguished trajectories are identified as traveling waves of the new system. In the other, they are steady states. There is some method in our madness. This can be carried out for certain partial differential equations, which when viewed as a dynamical system, are naturally infinite-dimensional. The point is that the system in the space of trajectories is actually an ODE.
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