In this paper, we study the physical measures for a class of partially hyperbolic flows with mostly contracting centre. Let X be a $C^2$ vector field on a compact Riemannian manifold M with partially hyperbolic splitting $TM=E^u\oplus E^c$. We prove that if the centre direction $E^c$ exhibits the asmptotically sectionally contracting behaviour with respect to Gibbs u-states, then X admits finitely many physical measures, and their basins cover Lebesgue almost all points of the ambient manifold. Moreover, when the unstable manifolds are dense, we prove that X admits only one physical measure whose basin covers a full Lebesgue measure subset. By tracing the physical measures via typical hyperbolic periodic orbits, we study the statistical stability of this kind of partially hyperbolic flows.

在本文中，我们研究了一类具有大部分收缩中心的部分双曲线流的物理测度。设X为$C^2$具有部分双曲分裂的紧黎曼流形M 上的向量场$吨米={乙}^{你}\oplus {乙}^C$. 我们证明如果中心方向${乙}^C$表现出关于 Gibbs u 态的渐近截面收缩行为，那么X 承认有限的许多物理测度，并且它们的盆地几乎覆盖了环境流形的所有点。此外，当不稳定流形密集时，我们证明X只承认一个物理测度，其盆地覆盖了一个完整的 Lebesgue 测度子集。通过典型的双曲周期轨道跟踪物理量度，我们研究了这种部分双曲流的统计稳定性。