Jörg Main
Publications:
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Kuchelmeister M., Reiff J., Main J., Hernandez R.
Dynamics and Bifurcations on the Normally Hyperbolic Invariant Manifold of a Periodically Driven System with Rank-1 Saddle
2020, vol. 25, no. 5, pp. 496-507
Abstract
In chemical reactions, trajectories typically turn from reactants to products when
crossing a dividing surface close to the normally hyperbolic invariant manifold (NHIM) given
by the intersection of the stable and unstable manifolds of a rank-1 saddle. Trajectories started
exactly on the NHIM in principle never leave this manifold when propagated forward or
backward in time. This still holds for driven systems when the NHIM itself becomes timedependent.
We investigate the dynamics on the NHIM for a periodically driven model system
with two degrees of freedom by numerically stabilizing the motion. Using Poincaré surfaces of
section, we demonstrate the occurrence of structural changes of the dynamics, viz., bifurcations
of periodic transition state (TS) trajectories when changing the amplitude and frequency of the
external driving. In particular, periodic TS trajectories with the same period as the external
driving but significantly different parameters — such as mean energy — compared to the
ordinary TS trajectory can be created in a saddle-node bifurcation.
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