论文标题
动态系统的箭量表示和降低尺寸
Quiver representations and dimension reduction in dynamical systems
论文作者
论文摘要
动态系统通常会接受研究其行为时必须考虑的几何特性。我们表明，许多这样的属性可以通过颤抖表示形式进行编码。这些属性包括经典的对称性，隐藏的对称性和前馈结构，以及网络动态系统中的子网和商关系。 Quiver Equivariant动力系统由一系列动态系统组成，它们之间的地图将解决方案发送到解决方案。我们证明，在Lyapunov-Schmidt还原，中心歧管还原和正常形式还原下保存了这种箭量结构。
Dynamical systems often admit geometric properties that must be taken into account when studying their behaviour. 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.
