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Mathematical Physics

arXiv:1307.1986 (math-ph)
[Submitted on 8 Jul 2013 ]

Title: Generalized notions of symmetry of ODE's and reduction procedures

Title: 常微分方程的对称性广义概念和约化过程

Authors:Giampaolo Cicogna
Abstract: This paper describes the notion of \sigma -symmetry, which extends the one of \lambda-symmetry, and its application to reduction procedures of systems of ordinary differential equations and of dynamical systems as well. We also consider orbital symmetries, which give rise to a different form of reduction of dynamical systems. Finally, we discuss how dynamical systems can be transformed into higher-order ordinary differential equations, and how these symmetry properties of the dynamical systems can be transferred into reduction properties of the corresponding ordinary differential equations. Many examples illustrate the various situations.
Abstract: 本文描述了\sigma -对称性的概念,它扩展了\lambda -对称性的概念,并将其应用于常微分方程组和动力系统的约化过程。我们还考虑了轨道对称性,它们导致了动力系统不同形式的约化。最后,我们讨论了如何将动力系统转化为高阶常微分方程,以及这些动力系统的对称性性质如何转化为相应常微分方程的约化性质。许多例子说明了各种情况。
Comments: 14 pages, no fig., Math. Meth. Appl. Sci. (ICNAAM Proc.), to appear
Subjects: Mathematical Physics (math-ph)
Cite as: arXiv:1307.1986 [math-ph]
  (or arXiv:1307.1986v1 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1307.1986
arXiv-issued DOI via DataCite
Journal reference: Math. Meth. Appl. Sci. (ICNAAM Proc.) 37, (2014) 1819-1827
Related DOI: https://doi.org/10.1002/mma.2937
DOI(s) linking to related resources

Submission history

From: Giampaolo Cicogna [view email]
[v1] Mon, 8 Jul 2013 08:59:09 UTC (12 KB)
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