Computing geometric Lorenz attractors with arbitrary precision
Computing geometric Lorenz attractors with arbitrary precision
复制标题
以任意精度计算几何洛伦兹吸引子
DOI：
10.1090/tran/7228
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Ning Zhong
中科院分区：
文献类型：
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作者：
D. Graça;Cristobal Rojas;Ning Zhong
Lorenz吸引子是由E. N. Lorenz是第一个奇怪吸引子的例子。然而，洛伦兹的研究主要是基于（非严格的）数值模拟，直到最近，洛伦兹吸引子存在的证明仍然难以捉摸。为了解决这个问题，一些作者引入了几何洛伦兹模型，并证明了几何洛伦兹模型有一个奇怪的吸引子。在2002年，原始的洛伦兹模型表现得像一个几何洛伦兹模型，因此有一个奇怪的吸引子。在本文中，我们表明几何洛伦兹吸引子是可计算的，以及它们的物理措施。
The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of \emph{strange attractors}. However Lorenz' research was mainly based on (non-rigourous) numerical simulations and, until recently, the proof of the existence of the Lorenz attractor remained elusive. To address that problem some authors introduced geometric Lorenz models and proved that geometric Lorenz models have a strange attractor. In 2002 it was shown that the original Lorenz model behaves like a geometric Lorenz model and thus has a strange attractor. In this paper we show that geometric Lorenz attractors are computable, as well as their physical measures.