论文标题
部分双曲线流的SRB措施，主要是扩展的中心
SRB measures for partially hyperbolic flows with mostly expanding center
论文作者
论文摘要
我们证明，具有二维中心的$ C^1 $向量场的部分双曲线吸引子支持SRB度量。此外，我们表明，如果矢量字段为$ c^2 $，并且中心捆绑包承认截面扩展条件W.R.T.任何Gibbs $ u $ $州，那么吸引子只能支持有限的许多SRB/物理措施，其盆地涵盖了Lebesgue几乎所有拓扑盆地的所有点。这些结果的证明必须处理在差异性的情况下不会出现的困难。
We prove that a partially hyperbolic attractor for a $C^1$ vector field with two dimensional center supports an SRB measure. In addition, we show that if the vector field is $C^2$, and the center bundle admits the sectional expanding condition w.r.t. any Gibbs $u$-state, then the attractor can only support finitely many SRB/physical measures whose basins cover Lebesgue almost all points of the topological basin. The proof of these results has to deal with the difficulties which do not occur in the case of diffeomorphisms.
