In my rough understanding Molecular Dynamics using Classical Newtonian mechanics is a 6N dimensional non linear system. 6N dimension because we have 3 position vectors and 3 momentum vectors for each N particles. Nonlinearity because of the terms in force fields as far as I understand. In principle this system can exhibit chaos. So my question is the following: Is there any scenario where by the system enters a stable/ semi stable limit cycle or periodic trajectory? I have read that the system cannot go into a point attractor since the volume of probability density function must be conserved and cannot become zero. If the system can enter periodic oscillations or limit cycle what does that imply?
UPDATE : Can someone give me reference suggestions like books, papers, video lectures or any other document links related to this topic? I also wanted to know whether the assumption of ergodicity in the system prohibits limit cycles ?
( @Wrzlprmft answered my question about ergodicity in chats. I am copying it here :
In case of a system with attractors, you can consider ergodicity as follows: On the one hand you take one arbitrary condition, evolve it for some time (to discard transients) and then start pooling the ensuing trajectory for the time average. On the other hand you take a bunch of arbitrary initial conditions, evolve them for some time (to discard transients) and pool the resulting states (one per initial condition) to obtain the ensemble average. In case of a single attractor, the time and ensemble average are the same, namely the average over all states on the attractor. In case of two or more attractors, the time average only reflects the states of one attractor, while the ensemble average reflects the states of all attractors. Hence such systems are not ergodic. )