论文标题
主要是分段扩展流的物理措施
Physical measures for mostly sectional expanding flows
论文作者
论文摘要
我们证明，部分双曲线吸引在C2矢量场中设置为平衡的缓慢复发，并在捕获区域允许在阳性LEBESGUE MATER MEATER MEAMES集中进行非均匀的截面扩张，从而支持Ergodic物理/SRB测量。此外，在这种情况下，吸引集的支持最多有限的许多千古/SRB措施，它们也是沿着中心不稳定方向的吉布斯状态。 这扩展到连续的时间系统，对于差异性，获得了类似的众所周知的结果，其中包括在吸引集合中常规轨道积累的平衡的存在。在串联两个中，相同的结果成立，假设捕获区域上的trajetories在正体积子集中接受了渐近截面膨胀的时间序列。 我们提供了几个应用程序的例子，包括存在渐近截面双曲线吸引集的物理措施，并以替代统一的方式获得许多已知示例的物理措施：洛伦兹（Lorenz）类似洛伦兹（Lorenz）和罗维拉（Rovella）吸引子，以及分类的纤维性吸引人吸引套件（包括多维洛伦兹吸引者）。
We prove that a partially hyperbolic attracting set for a C2 vector field, having slow recurrence to equilibria, supports an ergodic physical/SRB measure if, and only if, the trapping region admits non-uniform sectional expansion on a positive Lebesgue measure subset. Moreover, in this case, the attracting set supports at most finitely many ergodic physical/SRB measures, which are also Gibbs states along the central-unstable direction. This extends to continuous time systems a similar well-known result obtained for diffeomorphisms, encompassing the presence of equilibria accumulated by regular orbits within the attracting set. In codimension two the same result holds, assuming only the trajetories on the trapping region admit a sequence of times with asymptotical sectional expansion, on a positive volume subset. We present several examples of application, including the existence of physical measures for asymptotically sectional hyperbolic attracting sets, and obtain physical measures in an alternative unified way for many known examples: Lorenz-like and Rovella attractors, and sectional-hyperbolic attracting sets (including the multidimensional Lorenz attractor).
