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Normal Form for Systems with Linear Part <i>N</i><sub>3(<i>n</i>)</sub>
Department of Mathematics, Kimathi University College of Technology, Nyeri, Kenya
Department of Mathematics, Kenyatta University, Nairobi, Kenya
Pure and Applied Mathematics (PAM) Department, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
- 1 Department of Mathematics, Kimathi University College of Technology, Nyeri, Kenya
- 2 Department of Mathematics, Kenyatta University, Nairobi, Kenya
- 3 Pure and Applied Mathematics (PAM) Department, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Applied Mathematics·Volume 03 (2012)·Pages 1641–1647·Published 7 November 2012·DOI10.4236/am.2012.311227
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Abstract
The concept of normal form is used to study the dynamics of non-linear systems. In this work we describe the normal form for vector fields on 3 × 3 with linear nilpotent part made up of coupled R 3n Jordan blocks. We use an algorithm based on the notion of transvectants from classical invariant theory known as boosting to equivariants in determining the normal form when the Stanley decomposition for the ring of invariants is known.
KeywordsTransvectantEquivariantsBox ProductStanley Decomposition
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