标题： 大部分非一致横截扩张系统 显示英文标题

标题： Mostly nonuniformly sectional expanding systems

摘要： 在本文中，我们引入了奇异流的大部分非一致横截扩张（MNUSE）概念，该概念包含众所周知的横截双曲性以及新的定义，即渐近横截双曲性和多奇异双曲性。我们展示了一个非一致横截双曲集的例子，在这种新意义上，它既不是$2$-横截双曲的，也不是渐近横截双曲的，证明这是一个更广泛的奇异流的弱双曲性概念。此外，在$C^2$设置下，根据中心子丛的维数或Lyapunov指数符号的一些假设，我们证明吸引的MNUSE集支持一个物理/SRB测度。并且该测度对于MNUSE吸引子是唯一的。 显示英文摘要

摘要： In this note, we introduce the notion of mostly nonuniform sectional expanding (MNUSE) for singular flows which contains the well known sectional hyperbolicity as well new definitions as asymptotically sectional and multisingular hyperbolicities. We exhibit an example of nonuniformly sectional hyperbolic set, in this new sense, which is neither $2$-sectional hyperbolic nor asymptotically sectional hyperbolic, proving that this is a broader notion of weak hyperbolicity for singular flows. Moreover, in $C^2$ setting, under some assumptions of either the dimension or the sign of Lyapunov exponents of the central subbundle, we prove that attracting MNUSE sets support a physical/SRB measure. And this measure is unique for MNUSE attractors.