Chaotic transitions global dynamics

The mechanism of these transitions is nontrivial and has been discussed in detail elsewhere Q, 12) it involves the development of a homoclinic tangencv and subsequently of a homoclinic tangle between the stable and unstable manifolds of the saddle-type periodic solution S. This tangle is accompanied by nontrivial dynamics (chaotic transients, large multiplicity of solutions etc.). It is impossible to locate and analyze these phenomena without computing the unstable, saddle-tvpe periodic frequency locked solution as well as its stable and unstable manifolds. It is precisely the interactions of such manifolds that are termed global bifurcations and cause in this case the loss of the quasiperiodic solution. 

In typical molecular dynamics applications with multiple bodies and complicated force laws, the motion is assumed to be chaotic. Ergodic coverage of would then have to arise from the global properties of a chaotic system (sensitivity to initial conditions and transitivity). Liouville s equation,... 

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