In chapter 1 we cite the GitHub repository of the book. Part of this repository is the very nice ability to have open discussion on potential things that are incorrect in the book (such as typos), or sections that may be better explained or missing. So, in the book we should actively motivate readers to contribute/open issues on this GitHub page!

(we only cite the GitHub page, but we don't present it with its full potential)

The story of "Climate attractors", which is discussed in Sect. 12.3.2 has more meat to it than we attribute to it in our Further reading sections. Worth noting is particularly:

• Tsonis, A. A., Elsner, J. B., & Georgakakos, K. P. (1993). Estimating the Dimension of Weather and Climate Attractors: Important Issues about the Procedure and Interpretation. Journal of the Atmospheric Sciences, 50(15), 2549–2555. https://doi.org/10.1175/1520-0469(1993)050<2549:ETDOWA>2.0.CO;2 , which summarizes a bit the story and the problems.
• Badin, G., & Domeisen, D. I. V. (2014). A Search for chaotic behavior in Northern Hemisphere stratospheric variability. Journal of the Atmospheric Sciences, 71(4), 1494–1507. https://doi.org/10.1175/JAS-D-13-0225.1 , which summarises the story much better and gives an apparently completely list of the arguments, counter arguments, and counters to the counter arguments.

Something we don't mention, but we should, is that there have been raised counter arguments to the original rebuttals by Grassberger-Procaccia, saying that in fact the limit of datapoints is much lower than what originally thought of. This is discussed in the Tsonis reference. Unfortunately, I've read the paper, but I remain unconvinced, because it uses a logically flawed circular argument to claim "smaller amount of points necessary". Still, we must be as transparent as possible.

Furthermore, what Badin and Domeisen argue, and what Lorenz already argued in 1991 (reference cited in chapter 12), is that while it may not make sense to try to estimate the dimension of a "climate attractor", it could be possible to estimate such a dimension for a somewhat isolated climate subsystem.

It came to my attention that some students read our Chapter 1 and the use the very first code snippet to make their own dynamical system. That is great if the system is sufficiently low dimensional. However, some students use the same code to make any dynamical system, such as e.g., a coupled oscillator network which could be arbitrarily high dimensional.

We should have a clear note in that section warning about this. Something like:

Note that Code 1.1 is meant to be used when the dynamical system is low dimensional. For high dimensional systems an alternative code should be used that is described in the documentation of DynamicalSystems.jl

Figure 8.2b shows the boundary map of a mushroom billiard, with a chaotic and two regular trajectories and the regular island shaded in gray. However, the shaded area seems to be too small: one of the regular trajectories (the teal one) is outside the regular island in the cap.
Looking at the dimensions of this mushroom, the sin(θ) of the chaotic band in the cap should be within ±0.1 (the critical angle is sin(θ_c) = w/2R).

This error can't be reproduced with the corresponding script in this repo (8.3.jl) since the shading seems to be a later addition.

Please post here all typos you have found in the first edition of the book.

After working with students on using mutual information, and referring them to our book, I realized that it was not clear to them what the summants n, m are in equation 7.1. The summation goes over bins, while the students were summing over the indices of x and y.

I think our text does not explain enough the MI. It defines it and proceeds immediatelly to discuss its properties, but I think we should spend a couple of sentences discussing what the summation means and how one does it in practice.