It is actually one of the nice facts of life that as you dial up the local instability of a dynamical system you get a corresponding increase in the statistical stability. As systems become more and more chaotic they act more and more like iid coin tosses, which we understand quite well.
"It is actually one of the nice facts of life that as you dial up the local instability of a dynamical system you get a corresponding increase in the statistical stability."
I am a mathematician working in a tangentially related area and have never come across this before.
And yes it is very interesting. One can actually model iid coin flips (or dice rolls) as a type of expanding dynamical system called a full-shift.
"This approach of interpreting the stability of the system by linearizing it near the equilibrium does not tell much about a system’s asymptotic behavior at large."
