An algebraic approach for obtaining nilpotent normal forms in dimension 4

Autor:	Weiyi Zhang, K. Huseyin
Rok vydání:	2000
Předmět:	Pure mathematics Nilpotent Partial differential equation Series (mathematics) Differential equation Applied Mathematics Homogeneous polynomial Mathematical analysis Physical system Algebraic number Algebraic normal form Mathematics
Zdroj:	IMA Journal of Applied Mathematics. 64:109-123
ISSN:	1464-3634 0272-4960
Popis:	In this paper, an algebraic approach is presented for determining the normal forms of four-dimensional systems with a nilpotent linear part. Certain transformations introduced in this case result in a simplified procedure for the calculation of normal forms. Thus, one does not need to solve a series of partial differential equations as usually required by the normal-form theory; indeed, algebraic calculations are sufficient. The approach can be applied to higher-order systems with a nilpotent linear part as well. To illustrate the new approach, five examples are presented. Normal forms and the associated coefficients of two physical systems, an electric network and a mechanical system, are fully analyzed.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::58727a610588318510395eccb34bd81b https://doi.org/10.1093/imamat/64.2.109 Zobrazit plný text záznamu