2
$\begingroup$

I do not quite understand the idea of an integrable dynamical system. Does it mean that the EOMs are analytically and exactly solvable? What are the necessary and sufficient conditions such that a system is integrable?

$\endgroup$

2 Answers 2

4
$\begingroup$

There has been extensive discussion on this here. Infact the question was posed by Gil Kalai, a well known mathematician. I hope it helps.

$\endgroup$
2
$\begingroup$

For mathematicians the question is very hard, for physicists the following jargon is used to intuitively define integrability: solvable=integrable, separable=integrable, existence of a Lax pair=integrable, # of conserved quantities equats to # of degrees of freedom = integrable.

It is interesting that the mathematicians have managed to find the exceptions to all the intuitive definitions. In general the most general physical definition is the following: if there is no of chaos then the system is integrable.

For more information look at Zakharov V.E. What is integrability (Springer, 1992).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.