论文标题
强大的指数混合和融合到平衡的奇异双曲线吸引集
Robust Exponential Mixing and Convergence to Equilibrium for Singular Hyperbolic Attracting Sets
论文作者
论文摘要
我们扩展了几何洛伦兹吸引子的稳健指数混合的结果，具有茂密的轨道和独特的奇异性，到具有任何数量的（Lorenz-或非洛伦兹（Lorenz）或类似洛伦兹（Lorenz）的奇异性）的奇异型纤维吸引力，有一定程度地吸引人的态度，并且有一定程度地吸引了许多奇特的人/srb物理/srb的物理概率的概率。我们获得了捕获区域支持的任何物理概率度量的指数混合，也可以获得指数融合到均衡的指数，对于任何$ c^2 $开放子集中的矢量字段中的任何$ d $ d $ d $二维紧凑型歧管（$ d \ ge3 $）。
We extend results on robust exponential mixing for geometric Lorenz attractors, with a dense orbit and a unique singularity, to singular-hyperbolic attracting sets with any number of (either Lorenz- or non-Lorenz-like) singularities and finitely many ergodic physical/SRB invariant probability measures, whose basins cover a full Lebesgue measure subset of the trapping region of the attracting set. We obtain exponential mixing for any physical probability measure supported in the trapping region and also exponential convergence to equilibrium, for a $C^2$ open subset of vector fields in any $d$-dimensional compact manifold ($d\ge3$).
