Generalized critical points analysis of acetylene vibrational dynamics
  Classical tools of nonlinear dynamics are used to study the highly excited vibrations of small molecules. For effective Hamiltonians with one polyad number (approximate constant of motion), previously developed methods locate new anharmonic modes using the critical points in the reduced classical phase space. Theoretical arguments are given for generalizing the method to more than one polyad number.   The pure bending Hamiltonian of acetylene is analyzed to demonstrate the effectiveness of critical points analysis. Four families of critical points are born in distinct bifurcations, each corresponding to a novel anharmonic mode. These modes are visualized with custom computer-generated animations.   The same analysis is extended for the first time to the acetylene stretchbend system, which has never been analyzed classically with all the resonance couplings. Preliminary results are obtained for the polyad series containing the C-H stretch overtones. 
V. Tyng