Foundations of Computational Mathematics

, Volume 13, Issue 4, pp 479–516 | Cite as

Scaling Invariants and Symmetry Reduction of Dynamical Systems

Article

Abstract

Scalings form a class of group actions that have theoretical and practical importance. A scaling is accurately described by a matrix of integers. Tools from linear algebra over the integers are exploited to compute their invariants, rational sections (a.k.a. global cross-sections), and offer an algorithmic scheme for the symmetry reduction of dynamical systems. A special case of the symmetry reduction algorithm applies to reduce the number of parameters in physical, chemical or biological models.

Keywords

Group actions Rational invariants Matrix normal form Model reduction Dimensional analysis Symmetry reduction Equivariant moving frame 

Mathematics Subject Classification

08-04 12-04 14L30 15-04 

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Copyright information

© SFoCM 2013

Authors and Affiliations

  1. 1.INRIA MéditerranéeSophia AntipolisFrance
  2. 2.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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