Invariant Manifolds Mediating Collinear Hydrogen Exchange Reaction

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We discuss the phase space structure for the collinear hydrogen exchange system crosses an energy barrier. Above the reaction threshold, the system must pass through a Symmetric Stretch Periodic Orbit (SSPO) where the dynamics are structuring a Dividing Surface (DS), that separates reactants and products. At low energy, the SSPO can serve as a dividing surface that satisfies the no-recrossing assumption of Transition State Theory (TST). As the energy increases, saddle-node bifurcations occur on both sides of the SSPO. Above the bifurcation energy, trajectories appear that recross the central DS. The region of recrossing trajectories is bounded by the stable manifolds of the additional Unstable Periodic Orbits (UPOs). We investigate the fractal structure of the TST violating islands of the DS and how it is determined by the invariant manifolds of the additional periodic orbits. We demonstrate that the various layers are all bounded by the same stable manifold.