论文标题
关于奇异的奇异刺激性吸引套装的千古型物理/SRB测量的数量
On the number of ergodic physical/SRB measures of singular-hyperbolic attracting sets
论文作者
论文摘要
众所周知，在有限的尺寸紧凑型歧管上以$ c^2 $流动的截面式纤维吸引集，最多有许多有限的Ergodic物理不变概率指标。我们证明了一个上限，用于在连接的奇异式纤维吸引力下以$ 3 $流的方式支撑的不同千古物理测量的数量。这种结合仅取决于吸引集中包含的洛伦兹样平衡的数量。提供了奇异的填充吸引套件的例子，表明界限很锋利。
It is known that sectional-hyperbolic attracting sets, for a $C^2$ flow on a finite dimensional compact manifold, have at most finitely many ergodic physical invariant probability measures. We prove an upper bound for the number of distinct ergodic physical measures supported on a connected singular-hyperbolic attracting set for a $3$-flow. This bound depends only on the number of Lorenz-like equilibria contained in the attracting set. Examples of singular-hyperbolic attracting sets are provided showing that the bound is sharp.
