Question about the KAM theorem

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The discussion centers on the application of the KAM theorem to analyze chaotic motion in a Hamiltonian system with a nonlinear perturbation. The user has observed chaotic behavior at a perturbation parameter of 0.2 and seeks to determine the threshold for chaos analytically. The overlap criterion by Chirikov is mentioned as a relevant tool for this analysis. The recommended approach involves transforming to action-angle coordinates and expanding the perturbation in Fourier series.

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I have an Hamiltonian with a non linear perturbation attached to it. When the perturbation parameter equals .2 the system at a certain initial condition exhibits chaotic motion. I found this out graphically. I would like to calculate how large my perturbation parameter has to be analytically for the system to exhibit chaos. Would I use the KAM theorem for such a calculation? Any help will be much appreciated.
 
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There is the overlap criterion developed by Chirikov: link.

The general procedure is to go to the action-angle coordinates of the integrable system, and then having written the perturbation in terms of these variables expand it in Fourier series.
 

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