Can Phase Trajectories Intersect with Equilibria in Dynamical Systems?

[enricfemi]

Generally speaking, phase trajectories can not intersect in any dimension phase space.
But how about rest points. can trajectories truly entry equilibria.

THX!

 

[dx]

The phase trajectories close to equilibrium points are little circles around them. They don't intersect each other. The phase trajectory of a system in equilibrium is just a point.

 

[enricfemi]

but it sounds strange that no trajectory intersect with equilibrium.
there are some other kinds of equilibrium points, like spiral point, which seems not just circles around point.
Is that finally attach equilibrium, since i cannt find any good reason that why equilibrium should be isolate?