关于三维流对初始条件的敏感依赖性和物理测度的存在性
On sensitive dependence on initial conditions and existence of physical measure for 3-flows
摘要：
在回顾了关于吸引子的敏感性和鲁棒性的已知结果以及对它们的证明的观察之后，我们表明，对于三维流的吸引子，鲁棒混沌行为（意味着对所有邻近流的过去和未来的初始条件的敏感性）等价于某些双曲结构的存在。这些结构反过来又与有形措施的存在有关。简而言之，在低维情况下，光滑流的鲁棒混沌行为确保了物理测量的存在。
英文摘要：
After reviewing known results on sensitiveness and also on robustness of attractors together with observations on their proofs, we show that for attractors of three-dimensional flows, robust chaotic behavior meaning sensitiveness to initial conditions for the past as well for the future for all nearby flows) is equivalent to the existence of certain hyperbolic structures. These structures, in turn, are associated to the existence of physical measures. In short in low dimensions, robust chaotic behavior for smooth flows ensures the existence of a physical measure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
