There’s a saying in mathematics circles which I’ll butcher here: “everything is either a linear system, reducible to linear systems, or unapproachable.”
Think about how bad we are at analytically solving “simple looking” diff-eqs and the above statement starts to sound too true.
Exactly. Finding a few hundred periodic orbits is a lot of hard work but you don’t have the glory of having “solved” something. Because of that kind of thinking there are many unanswered questions which are ignored because they don’t seem to be part of some masterstroke.
Think about how bad we are at analytically solving “simple looking” diff-eqs and the above statement starts to sound too true.