We live in a boring planetary system. Can you imagine if we lived in one of those choreographies how difficult would it be for Kepler to devise the laws of planetary motion?
For one, the science is dead wrong. Just because the three body problem doesn't have an analytical solution that doesn't mean that orbits are chaotic. Case in point: the very solar system in question is now known to have at least one planet in a very stable orbit. Nor does it mean that they are particularly difficult to calculate in many circumstances. You just can't use algebraic methods. So I was turned off because the what-if proposed was fantasy not science fiction. Fwiw I had the same response to the movie Arrival, which many people seemed to love.
Second, the proposed solution that allows for the aliens to predict future seasons and therefore develop culture and technology reflects human problem solving. This is intellectually lazy and wrong. A more realistic solution, of the type I prefer to read about, would have the aliens evolve different ways of thinking that are more compatible with iterative methods than algebraic manipulation. To such a mind abstract reasoning would be really difficult, but it would be entirely natural to specify initial conditions and solve iteratively. Such a mind would find solving ordinary differential equations as easy as breathing, but solving x + 3 = 4 would need a computer. Even more interestingly, how would those differences in mind structure reflect the development of their language, culture, and societal structure? These are all very fascinating questions that seemed extremely obvious to me from the setup, and the sort of thing many hard sci-fi authors like Raynolds or Clarke would tackle. It's a book I would read and rave about. But instead we get the same old trope of basically human aliens invading earth because it is "habitable", never mind that habitability should be a non-concern to any self-respecting interstellar species, for whom climbing down a gravity well is probably a net negative. Planets are in fact shitty places to live in terms of galactic real estate, even more so when they are infected by foreign biology.
Finally, the behavior of humans across the entire books is utterly unrelatable. I'm limited in how much I can say without spoiling the story. But in short every scientist is portrayed as incurious (wtf?) nihilist easily swayed by the suggestion to kill all humans. And the rest of humanity hardly dares better -- they willingly and dejectedly walk to their own execution when they are told to later in the series. I have no explanation of this other than bad writing.
http://www.maths.manchester.ac.uk/~jm/Choreographies/
...plus a link to the animations for the linked paper:
http://numericaltank.sjtu.edu.cn/three-body/three-body.htm