Let X be a recurrent point of a planar system, that is, there is a sequence tn →±[infinity] such that φtn (X) → X. (a) Prove that either X is an equilibrium or X lies on a closed orbit. (b) Show by example that there can be a recurrent point for a nonplanar system that is not an equilibrium and does not lie on a closed orbit.

table a is wierd

step-by-step explanation:

6*f

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)

you need to add a picture

you would need to also lose 1 point for each of the other outcomes for it to be fair.

step-by-step explanation: