KAM theorem

sanctus · 04-27-2005

What are the most interesting consequences of the Kam theorem? I've to present it next week and I know some consequence (stability of solar system over next million years,etc), but I wondered if there were some really (more) astonishing ones to show?

Tormod · 04-27-2005

It would be very helpful if you could share with us what the Kam theorem is.

sanctus · 04-27-2005

The thm says: If we consider an autonomous system wich is non degenerate and we apply an autonomous perturbation. We have that if the perturbations is weak enough, the majority of the non-resonnant invariant tori doesn't disappear but are slightly deformed.[...]

As you see it is quite complicated (I didn't translate the second part). This thm comes from chaotic dynamics and it sort of states that if a system evolves on a tore (which is the case of many systems in a proper choice variables) when perturbed it rests on a tore. I haven't understood it yet well enough to be able to explain it in a simple way, this will come before next tuesday as I present it then....