- #1

ShayanJ

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## Main Question or Discussion Point

I wanna know is my understanding on PB theorem correct or not. What I understand is, if I define a differentiable real dynamical system on an open subset of plane(so the theorem only applies to dynamical systems in 2 spatial dimensions), the system, as [itex] t\to \infty [/itex], will have only one of the following behaviours:

1) Stands still at a point.

2) Moves periodically.

3) Moves from one equilibrium point to another with no periodicity.

Thanks

1) Stands still at a point.

2) Moves periodically.

3) Moves from one equilibrium point to another with no periodicity.

Thanks