Nathan Guillery
Publications:
Guillery N., Meiss J. D.
Diffusion and Drift in VolumePreserving Maps
2017, vol. 22, no. 6, pp. 700–720
Abstract
A nearlyintegrable dynamical system has a natural formulation in terms of actions, $y$ (nearly constant), and angles, $x$ (nearly rigidly rotating with frequency $\Omega(y)$). We study angleaction maps that are close to symplectic and have a twist, the derivative of the frequency map, $D\Omega(y)$, that is positivedefinite. When the map is symplectic, NekhoroshevЃfs theorem implies that the actions are confined for exponentially long times: the drift is exponentially small and numerically appears to be diffusive. We show that when the symplectic condition is relaxed, but the map is still volumepreserving, the actions can have a strong drift along resonance channels. Averaging theory is used to compute the drift for the case of rank$r$ resonances. A comparison with computations for a generalized Froeschlé map in fourdimensions shows that this theory gives accurate results for the rankone case.
