Normal Forms and Unfoldings for Local Dynamical Systems Rutilius Taurus Aemilianus in September 2008

in September 2008

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Normal Forms and Unfoldings for Local Dynamical Systems Rutilius Taurus Aemilianus in September 2008The subject of local dynamical systems is concerned with the following two questions: 1. Given an nn matrix A, describe the behavior, in a neighborhood of the origin, of the solutions of all systems of di? erential equations having a rest point at the origin with linear part Ax, that is, all systems of the form x ? = Ax+ , n where x? R and the dots denote terms of quadratic and higher order. 2.