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Quiver Representations and Dimension Reduction in Dynamical Systems
SIAM Journal on Applied Dynamical Systems ( IF 2.1 ) Pub Date : 2020-11-02 , DOI: 10.1137/20m1345670
Eddie Nijholt , Bob W. Rink , Sören Schwenker

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2428-2468, January 2020.
Dynamical systems often admit geometric properties that must be taken into account when studying their behavior. We show that many such properties can be encoded by means of quiver representations. These properties include classical symmetry, hidden symmetry, and feedforward structure, as well as subnetwork and quotient relations in network dynamical systems. A quiver equivariant dynamical system consists of a collection of dynamical systems with maps between them that send solutions to solutions. We prove that such quiver structures are preserved under Lyapunov--Schmidt reduction, center manifold reduction, and normal form reduction.


中文翻译:

动态系统中的颤振表示和降维

SIAM应用动力系统杂志,第19卷,第4期,第2428-2468页,2020年1月。
动力学系统通常会接受研究其行为时必须考虑的几何特性。我们展示了许多这样的属性可以通过颤抖表示来编码。这些属性包括经典对称性,隐藏对称性和前馈结构,以及网络动力学系统中的子网和商关系。颤动等变动力系统由动力系统的集合组成,动力系统之间具有将解决方案发送到解决方案的映射。我们证明在Lyapunov-Schmidt约简,中心流形约简和法线形式约简下保留了此类颤振结构。
更新日期:2020-11-02
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