Scaling Invariants and Symmetry Reduction of Dynamical Systems

Evelyne Hubert 1 George Labahn 2
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
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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Evelyne Hubert, George Labahn. Scaling Invariants and Symmetry Reduction of Dynamical Systems. Foundations of Computational Mathematics, Springer Verlag, 2013, 13 (4), pp.479-516. ⟨http://link.springer.com/article/10.1007%2Fs10208-013-9165-9⟩. ⟨10.1007/s10208-013-9165-9⟩. ⟨hal-00668882v2⟩

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