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1. Feb 24, 2017

### Kelly Lam

How does the adiabatic invariance of actions J imply that closed orbits remain closed when the potential is deformed adiabatically?

Is it because a closed orbit has commensurate angular frequencies $$\omega_i$$ defined by $$\omega_i = \frac{\partial H}{\partial J_i}$$ where H is the Hamiltonian, $$H=H(J)$$. And since the actions Js are invariant, the angular frequencies remain commensurate as the potential is adiabatically deformed, thus the orbit remains closed?

2. Mar 1, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.