论文标题
非汉密尔顿系统的普通马斯洛夫指数
Generalized Maslov indices for non-Hamiltonian systems
论文作者
论文摘要
我们将Maslov索引的定义扩展到了一类广泛的非Hamiltonian动力系统。为此，我们介绍了一个拓扑空间（我们称为Maslov-Arnold空间）与Lagrangian Grassmannian共享关键的拓扑特征，因此接受类似的索引理论。这个家庭包含拉格朗日格拉曼尼亚人，还有更多。我们构建了一个称为“超平面马斯洛夫 - 阿诺德空间”的示例家族，它们在司芒尼亚语中密集，因此比拉格朗日格拉曼尼亚人大得多（这是阳性编织的子序列）。然后将所得指数用于研究非对称反应扩散系统的特征值问题。我们分析的一个亮点是对图灵不稳定性的拓扑解释：随着扩散系数的比率增加的分叉对应于广义MASLOV指数的变化。
We extend the definition of the Maslov index to a broad class of non-Hamiltonian dynamical systems. To do this, we introduce a family of topological spaces--which we call Maslov-Arnold spaces--that share key topological features with the Lagrangian Grassmannian, and hence admit a similar index theory. This family contains the Lagrangian Grassmannian, and much more. We construct a family of examples, called hyperplane Maslov-Arnold spaces, that are dense in the Grassmannian, and hence are much larger than the Lagrangian Grassmannian (which is a submanifold of positive codimension). The resulting index is then used to study eigenvalue problems for non-symmetric reaction-diffusion systems. A highlight of our analysis is a topological interpretation of the Turing instability: the bifurcation that occurs as one increases the ratio of diffusion coefficients corresponds to a change in the generalized Maslov index.
