抛物型PDE的单位体积拓扑熵的定义与测量
The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's
摘要：
我们定义了单位体积的拓扑熵在抛物型偏微分方程，如复杂的Ginzburg-Landau方程，并表明它的存在，并有界的上Hausdorff维数倍的最大膨胀率。然后，我们给出了一个建设性的实施，这样的方程的惯性范围上的约束。使用这个界限，我们能够提出一个有限的采样算法，允许（原则上）从实验数据来测量这个熵。
英文摘要：
We define the topological entropy per unit volume in parabolic PDE's such as the complex Ginzburg-Landau equation, and show that it exists, and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allows (in principle) to measure this entropy from experimental data.
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。
