sanctus Posted April 27, 2005 Report Share Posted April 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? Quote Link to comment Share on other sites More sharing options...
Tormod Posted April 27, 2005 Report Share Posted April 27, 2005 It would be very helpful if you could share with us what the Kam theorem is. ;) Quote Link to comment Share on other sites More sharing options...
sanctus Posted April 27, 2005 Author Report Share Posted April 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.... Quote Link to comment Share on other sites More sharing options...
C1ay Posted April 27, 2005 Report Share Posted April 27, 2005 It would be very helpful if you could share with us what the Kam theorem is. ;)Here at MathWorld.... Quote Link to comment Share on other sites More sharing options...
Tormod Posted April 27, 2005 Report Share Posted April 27, 2005 Okay, thanks. Chaos theory? I would be very interested in hearing what you learn, but this is one area where I cannot offer any help... ;) Quote Link to comment Share on other sites More sharing options...
UncleAl Posted April 27, 2005 Report Share Posted April 27, 2005 Google"digital orrery" instability 36 hits"digital orrery" chaotic 226 hits"digital orrery" 703 hits Quote Link to comment Share on other sites More sharing options...
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