回2l

“浓硫酸可以脱水，这是中学化学课就教过的知识，而在《普通化学》课上，我才知道这个简单反应，在最先进的纳米介孔材料制备技术中可以起到重要作用，宛如‘神来之笔’……”在校园论坛上，一位同学这样写道。

WHY IS SOUP SEARCHING SO USEFUL IN LIFE?
BECAUSE LIFE EVOLVES?

Since the logistic map is confined to an interval on the real number line, its dimension is less than or equal to unity. Numerical estimates yield a correlation dimension of 0.500±0.005 (Grassberger, 1983), for r ≈ 3.5699456 (onset of chaos). Note: It can be shown that the correlation dimension is certainly between 0.4926 and 0.5024.
Questions(from easy to hard):
Q1. Is the correlation dimension the same within the universality class? (numerically tested, probably yes)
Q2. What are the symbolic dynamics of the logistic map at the onset of chaos?
This figure may give some hints:

Fig 1. The difference between two orbits with a 10^-10 initial difference. The figure is ruler(0,1,1,2,1,2,2,3...)-like. A more precise description may be the exponential of the ruler sequence, where the base is the Feigenbaum constant α=2.502903...
Q3. How to define the invariant measure on the set in terms of symbolic dynamics?
Q4. Is the correlation dimension exactly 1/2? (could be computed by renormalization methods)
Known: the attractor is not a Cantor set with uniform measure, otherwise different notions of dimensions on the attractor should be equal.

Start a blog and seed it with material you would like to see. In a few weeks, check a search engine for more material like your blog. Gerhard "Get Machines To Tell You" Paseman, 2019.08.23.