论文标题
部分可观测时空混沌系统的无模型预测
Isospectral connections, ergodicity of frame flows, and polynomial maps between spheres
论文作者
论文摘要
我们表明，在闭合弯曲的riemannian歧管上，具有简单的长度光谱，Bochner Laplacian的频谱决定了向量束的同构类别和在低级别假设下的连接到量表。我们还表明，每当捆绑包不承认均匀降低时，在负曲率下延伸的框架上的帧流量会延伸，从而延伸了地球曲率。这是通过在实际代数几何形状中的球体之间表现出这些问题与多项式图的分类来实现的。
We show that on closed negatively curved Riemannian manifolds with simple length spectrum, the spectrum of the Bochner Laplacian determines both the isomorphism class of the vector bundle and the connection up to gauge under a low-rank assumption. We also show that flows of frames on low-rank frame bundles extending the geodesic flow in negative curvature are ergodic whenever the bundle admits no holonomy reduction. This is achieved by exhibiting a link between these problems and the classification of polynomial maps between spheres in real algebraic geometry.
