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The Application of Improved Recursive Formula for Computing Normal Forms of Four-Dimensional Nilpotent Dynamical Systems

In this paper, an explicit recursive formula of normal forms under nonlinear near-identity transformations is introduced. By solving a series of algebra equations with the aid of Maple, not only the coefficients of k order normal form and the associated nonlinear transformations but also high (>k) o... Full description

Journal Title: Applied Mechanics and Materials 2013, Vol.437 (Industrial Design and Mechanics Power II), p.27-31
Main Author: Guo, Lei
Other Authors: Li, Qun Hong , Song, Zi Gen
Format: Electronic Article Electronic Article
Language: English
Subjects:
Publisher: Zurich: Trans Tech Publications Ltd
ID: ISSN: 1662-7482
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title: The Application of Improved Recursive Formula for Computing Normal Forms of Four-Dimensional Nilpotent Dynamical Systems
format: Article
creator:
  • Guo, Lei
  • Li, Qun Hong
  • Song, Zi Gen
subjects:
  • Algebra
  • Computation
  • Computer programs
  • Dynamical systems
  • Mathematical analysis
  • Nonlinearity
  • Recursive
  • Transformations (mathematics)
ispartof: Applied Mechanics and Materials, 2013, Vol.437 (Industrial Design and Mechanics Power II), p.27-31
description: In this paper, an explicit recursive formula of normal forms under nonlinear near-identity transformations is introduced. By solving a series of algebra equations with the aid of Maple, not only the coefficients of k order normal form and the associated nonlinear transformations but also high (>k) order terms of the original equations can be obtained. An example about four-dimensional nilpotent dynamical system is given to show applicability of the recursive formula and the outline of symbolic computer programs is given to support application of the recursive formula.
language: eng
source:
identifier: ISSN: 1662-7482
fulltext: no_fulltext
issn:
  • 1662-7482
  • 1660-9336
  • 1662-7482
url: Link


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descriptionIn this paper, an explicit recursive formula of normal forms under nonlinear near-identity transformations is introduced. By solving a series of algebra equations with the aid of Maple, not only the coefficients of k order normal form and the associated nonlinear transformations but also high (>k) order terms of the original equations can be obtained. An example about four-dimensional nilpotent dynamical system is given to show applicability of the recursive formula and the outline of symbolic computer programs is given to support application of the recursive formula.
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abstractIn this paper, an explicit recursive formula of normal forms under nonlinear near-identity transformations is introduced. By solving a series of algebra equations with the aid of Maple, not only the coefficients of k order normal form and the associated nonlinear transformations but also high (>k) order terms of the original equations can be obtained. An example about four-dimensional nilpotent dynamical system is given to show applicability of the recursive formula and the outline of symbolic computer programs is given to support application of the recursive formula.
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