Henon-Heiles Hamiltonian

From a standard two-dimensional Henon-Heiles Hamiltonian, Ferrer et al. 

Mode-specific unimolecular decomposition has been observed in much of the theoretical work listed in table 8.1. In some cases more than one zero-order Hamiltonian is necessary to assign resonance states for an excited molecule. For the Henon-Heiles Hamiltonian two zero-order Hamiltonians are used to identify assignable resonances as either restricted processors (Q ) or quasiperiodic liberators (Q ) (Bai et al., 1983 Hose and Taylor, 1982). Similarly, Manz and co-workers (Bisseling et al., 1987 Joseph et al., 1988) assigned many stretching resonances of ABA molecules as either hyperspherical mode or local mode states. At the same energy, the 2" states for the Henon-Heiles Hamiltonian decay about an order of magnitude faster than the g states. 

Figure 9 Configuration-space plots of 12 low-order periodic orbits (POs) obtained from the Henon-Heiles Hamiltonian at = 0.1, surrounded by the equipotential curve y q, qz) Note that certain POs touch the equipotential curve (e.g., 1,...

Vendrell O, Meyer H-D (2011) Multilayer multiconfiguration time-dependent Hartree method implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine. J Chem Phys 134 044135... 

The diagnostic power of the time-dependent invariant manifolds Wu and Ws as separatrices between reactive and nonreactive trajectories was illustrated in Ref. 40 for the example of a driven Henon-Heiles system described by the Hamiltonian... 

A Simple 3-DOF Hamiltonian. An example that illustrates in a nontrivial way some of the statements above is the three-dimensional Henon-Heiles potential... 

The hierarchy of tori is theoretically predicted by the Poincare-Birkhoff theorem [10] in nearly integrable systems with two degrees of freedom. For instance, the hierarchy in the Henon-Heiles system represented by the Hamiltonian is shown in Fig. 1. 

Henon-Heiles and stadium Hamiltonians, which serve to explain the appearance and persistence of adiabatic states. 

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