论文标题
部分可观测时空混沌系统的无模型预测
Invariance principle and non-compact center foliations
论文作者
论文摘要
我们证明了对部分双曲线差异形态的所谓“不变性原理”的概括：如果不变的概率度量使其所有等于零的中心lyapunov指数等于零，那么该度量将接受中心崩解，而中心崩解是由稳定和不稳定的塑料不变的。这是因为系统通过紧凑的中心叶子承认叶面的系统而闻名，我们将其扩展到一个较大的类，其中包含离散的Anosov流。 我们使用结果来分类最大熵的度量，并研究物理措施，以扰动Anosov流动的一对图。
We prove a generalization of a so called "invariance principle" for partially hyperbolic diffeomorphisms: if an invariant probability measure has all its center Lyapunov exponents equal to zero then the measure admits a center disintegration that is invariant by stable and unstable holonomies. This was known for systems admitting a foliation by compact center leaves, and we extend it to a larger class which contains discretized Anosov flows. We use our result to classify measures of maximal entropy and study physical measures for perturbations of the time-one map of Anosov flows.
