The structure of Lorenz attractors
The structure of Lorenz attractors
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DOI：
10.1007/bf02684770
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发表时间：
1979-12
期刊：
影响因子：
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通讯作者：
Mathématiques DE L’I.H.É.S;Robert F. Williams
中科院分区：
文献类型：
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作者：
Mathématiques DE L’I.H.É.S;Robert F. Williams
8 - 3 ^ ofE。N. Lorenz[7]最近引起了很多关注（[3],[lo],[12]），部分原因是它与湍流的关系。Lorenz通过截断Navier-Stokes方程得到了这个系统；它提供了一个与Ruelle-Takens相对的奇怪吸引子的引人注目的例子。我们简要地介绍一下Ruelle-Takens的观点。为了观察到任何类型的运动，导致这种运动的一组初始条件必须是正测度的。这本质上说，运动必须被一个吸引子束缚。直到最近，数学家只知道两种类型的吸引子——稳态吸引子（或吸收子）和周期吸引子。因此，当一个持续运动被认为既非稳态也非周期性时，它就被称为随机运动。或者是“混沌53”，随机数学被用到。洛伦兹攻击的正是这个不合逻辑的结论；他的文章题为“决定论的非周期运动”（1963）。
8———3^ ofE. N. Lorenz [7] has attracted much attention ([3],[lo],[12]) lately, in part because of its relation to turbulence. Lorenz obtained this system by" truncating" the Navier-Stokes equation; it offers a striking example of a strange attractor, vis-a-vis Ruelle-Takens [n].We present the Ruelle-Takens idea briefly. In order that any type of motion be observable, the set of initial conditions leading to this motion must be of positive measure. This essentially says that the motion must be bound to an attractor. Until recently, mathematicians knew of only two types—steady state attractors (or sinks) and periodic attractors. Thus when a persistent motion was seen to be neither steady state nor periodic, it was termed ((random 9? or" chaotic 53, and stochastic mathematics was invoked. It is just this non sequitur that Lorenz was attacking; his article is entitled" Deterministic aperiodic motion53 (1963).