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
Or any row rank revealing form.
In particular a v =0 (respectively b v =0) when \(u+v\notin \mathbb {N}^{n}\).
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.
This was the case in the many (>40) models from mathematical biology we examined.
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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
Keywords
- Group actions
- Rational invariants
- Matrix normal form
- Model reduction
- Dimensional analysis
- Symmetry reduction
- Equivariant moving frame