Hamiltonian dynamical systems transport structure

STRUCTURE OF RESONANCES AND TRANSPORT IN MULTIDIMENSIONAL HAMILTONIAN DYNAMICAL SYSTEMS... 

MD simulations with a constant energy is nothing but Hamiltonian dynamics. Recent accumulation of MD simulations will certainly contribute to our further understanding of Hamiltonian systems, especially in higher dimensions. The purpose of this section is to sketch briefly how the slow relaxation process emerges in the Hamiltonian dynamics, and especially to show that transport properties of phase-space trajectories reflect various underlying invariant structures. 

For time-dependent Hamiltonian systems we chose in Section IVB to use a normal form that decouples the reactive mode from the bath modes, but does not attempt a decoupling of the bath modes. This procedure is always safe, but in many cases it will be overly cautious. If it is relaxed, the dynamics within the center manifold is also transformed into a (suitably defined) normal form. This opens the possibility to study the dynamics within the TS itself, as has been done in the autonomous case, for example in Ref. 107. One can then try to identify structures in the TS that promote or inhibit the transport from the reactant to the product side. 

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