Hypernormal form theory: foundations and algorithms |
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Authors: | James Murdock |
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Institution: | Department of Mathematics, Iowa State University, Ames, IA 50011, USA |
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Abstract: | Hypernormal forms (unique normal forms, simplest normal forms) are investigated both from the standpoint of foundational theory and algorithms suitable for use with computer algebra. The Baider theory of the Campbell-Hausdorff group is refined, by a study of its subgroups, to determine the smallest substages into which the hypernormalization process can be divided. This leads to a linear algebra algorithm to compute the generators needed for each substage with the least amount of work. A concrete interpretation of Jan Sanders’ spectral sequence for hypernormal forms is presented. Examples are given, and a proof is given for a little-known theorem of Belitskii expressing the hypernormal form space (in the inner product style) as the kernel of a higher-order differential operator. |
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Keywords: | Normal form Hypernormal form Unique normal form Dynamical system Equilibrium point Spectral sequence Nonlinear oscillator Matrix perturbation Stanley decomposition |
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