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I created this page shortly after taking a course in dynamical systems, and I haven't reviewed any of that material for well over a year, so I would appreciate if someone else who is more knowledgeable in the area could help fix something. Specifically, the beginning of the definition needs some expository information about the behavior of nonlinear dynamical systems near equilibrium points (and why the definition is given in terms of properties of a linearization near the equilibrium point).
I don't mean to bash the anonymous editor who thought they were fixing the article, because it was my fault that this was not better explained, but please do not change the technical details of a technical article unless you are knowledgeable in the subject. If the article sounds fishy, use the talk page. Exponential dichotomy, like the concept of hyperbolicity that it extends, is an important concept primarily for non-linear systems, which often don't have closed solutions and so for which qualitative properties (such as exponential dichotomy) of equilibrium points is extremely important. CyborgTosser (Only half the battle) 09:43, 22 December 2006 (UTC)