We show that a sectional-hyperbolic attracting set for a Hölder- $C^{1}$ vector field admits finitely many physical/SRB measures whose ergodic basins cover Lebesgue almost all points of the basin of topological attraction. In addition, these physical measures depend continuously on the flow in the $C^{1}$ topology, that is, sectional-hyperbolic attracting sets are statistically stable. To prove these results we show that each central-unstable disk in a neighborhood of this class of attracting sets is eventually expanded to contain a ball whose inner radius is uniformly bounded away from zero.

中文翻译：

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截面双曲线吸引集和统计稳定性的有限多物理度量

我们证明了 Hölder- 的截面双曲线吸引集$C^{1}$向量场允许有限的许多物理/SRB 测量，其遍历盆地几乎涵盖了拓扑吸引盆地的所有点。此外，这些物理措施持续依赖于$C^{1}$拓扑，即截面-双曲线吸引集在统计上是稳定的。为了证明这些结果，我们证明了在这类吸引集的邻域中的每个中心不稳定圆盘最终都会扩展为包含一个内半径均匀地远离零的球。