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Scaling Invariants and Symmetry Reduction of Dynamical Systems

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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.

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Notes

  1. Or any row rank revealing form.

  2. In particular a v =0 (respectively b v =0) when \(u+v\notin \mathbb {N}^{n}\).

  3. It is actually a differential system of Lie type: the entries of the Maurer–Cartan matrix [12] are the coefficients of the Lie algebra basis.

  4. This was the case in the many (>40) models from mathematical biology we examined.

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Correspondence to George Labahn.

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Communicated by Elizabeth Mansfield.

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Hubert, E., Labahn, G. Scaling Invariants and Symmetry Reduction of Dynamical Systems. Found Comput Math 13, 479–516 (2013). https://doi.org/10.1007/s10208-013-9165-9

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  • DOI: https://doi.org/10.1007/s10208-013-9165-9

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