论文标题
混合意味着在一个编码中混合一个双曲线吸引子和Anosov流动
Mixing implies exponential mixing among codimension one hyperbolic attractors and Anosov flows
论文作者
论文摘要
在任何维度$ d \ geq 3 $的紧凑型歧管上，我们表明，具有一维扩展方向的稳定且不稳定的叶子的共同不整合性，对于$ c^2 $的矢量场表示，这意味着指数与其物理度量有关。 因此，相对于其非平凡吸引子的物理度量，将$ c^1 $开放和$ c^2 $浓度的子集呈指数级的矢量场集合。 此外，对于编纂的一个$ c^2 $ anosov在任何维度上流动$ d \ geq 3 $，如果流动相对于唯一的物理措施混合，则流量为成倍混合，证明在这种情况下的Bowen-Ruelle猜想。
On a compact manifold of any dimension $d\geq 3$, we show that joint non-integrability of the stable and unstable foliation of a hyperbolic attractor with one-dimensional expanding direction, for a vector field of class $C^2$, implies exponential mixing with respect to its physical measure. Consequently, the set of Axiom A vector fields which mix exponentially with respect to the physical measure of its non-trivial attractors contains a $C^1$-open and $C^2$-dense subset of the set of all Axiom A vector fields. Moreover, for codimension one $C^2$ Anosov flows in any dimension $d\geq 3$, if the flow mixes with respect to the unique physical measure, then the flow mixes exponentially, proving the Bowen-Ruelle conjecture in this setting.
