Cvitanovic's book, and apparently Cvitanovic himself (I've traded an email or two, but he's friends of friends -and seems to always make a big impression in person) is amazing. It's been around in some form or other since I was wrapping up my ph.d. thesis in a related subject, and I remember being mad as hell it didn't exist when I started as it had the most understandable explanations of the Gutzwiller trace formula. The late Dieter Wintgen's papers were also good, but not as didactic, and without so many examples.
I should work out all the problem sets in J and publish the results. Seems like a properly impish trolling.
I've never had a strong incentive to read it, so I have only looked through it, but I love it. I fantasize about writing a book just like it on a subject that I know well.
The ability of an observer to keep track of things is not relevant, and even completely computable things like cellular automata can be chaotic [1]. The common definition of chaotic dynamics [2] requires the system to be sensitive to initial conditions, mix the state space, and have dense periodic orbits.
While there is a mathematical definition, there are uses of the term exactly described by you. For example, the Edge of Chaos (https://en.wikipedia.org/wiki/Edge_of_chaos) has a mathematical definition, but has been used in many additional areas because it so clearly seems to describe what happens as systems become so complex that they become effectively chaotic to a human's ability to order them. This edge can shift as tools improve and push back this edge.
Chaos is what happens when the torus in your dynamical phase space breaks up. Or, thought of another way; it's a deterministic process that generates random bit strings (because, no torus/periodic orbits).
I was hoping to read what's it about here in the comments, without opening the website, but ...
For people like me: It's a book about theory of chaos.
To quote:
> By now, there are also many physics textbooks on "chaos". Most lack depth, and many of them are plain bad, emphasizing pictorial and computer-graphics aspects of dynamics and short changing the student on the theory. That's a pity, as the subject in its beauty and intellectual depth ranks alongside statistical mechanics and quantum field theory, with which it shares many fundamental techniques. The book represents authors' attempt to redress the balance and present the subject as one of the basic cornerstones of the advanced graduate physics curriculum of future
Ah, I loved that book as a teen. Unfortunately I lent it to an ex whom I broke up with before she had returned it and never spoken with eversince.
I fondly remember tinkering with a PHP program (that was the only language I knew at the time ¯\_(ツ)_/¯) to draw the bifurcation diagram of the logistic map which then I used as my desktop background.
I should work out all the problem sets in J and publish the results. Seems like a properly impish trolling.