4 ms·
You misunderstand sensitive dependence on initial conditions, though admittedly it’s poorly elucidated in the article. It’s not about closed form solutions. It
by JackFr 5y ago
You misunderstand sensitive dependence on initial conditions, though admittedly it’s poorly elucidated in the article.
It’s not about closed form solutions. It’s about how neighborhoods on the line are mapped.
- pfortuny 5y agoThat does not matter: either the solutions are unique or not, and ODEs (out of singular points) have a unique aolution for any set of initial conditions. The sensitivity to initial conditions has nothing to do with regular ODEs and uniqueness.
- freemint 5y ago> ODEs (out of singular points) have a unique solution for any set of initial conditions I am not sure if that statement is to weak. In general you can only guarantee the solution of an explicit ODE over some interval if the right hand side is Lipschitz continuous.
- pfortuny 5y agoWell, yes. But the author is assuming it and his equations are C-infinity as a matter of fact.