The mapping is not 1-to-1, it's done via approximation, which means that what gets solved is not the original equation. And ... as I believe poincaré found out

The mapping is not 1-to-1, it's done via approximation, which means that what gets solved is not the original equation. And ... as I believe poincaré found out when he tried to apply series expansion to the 3 body problem, the devil (chaotic behavior) is in the long tail of the series coefficients [edit]: https://en.wikipedia.org/wiki/Poincar%C3%A9_and_the_Three-Body_Problem https://en.wikipedia.org/wiki/Poincar%C3%A9_and_the_Three-Bo... http://www.bourbaphy.fr/chenciner.pdf http://www.bourbaphy.fr/chenciner.pdf