Is there any nonempty, compact and invariant set in dynamical system generated by this system of equ

Rachel Villa

Rachel Villa

Answered question

2022-05-30

Is there any nonempty, compact and invariant set in dynamical system generated by this system of equations?
x = x + sin ( x y + 2 ) 7
My idea is to use this fact: Not empty omega limit set - because here we have also bounded functions and omega limit set is invariant. But it's hard to say anything about compactness.

Answer & Explanation

Brooks Butler

Brooks Butler

Beginner2022-05-31Added 9 answers

Hint: a fixed point is a compact invariant set. If that fixed point has a stable manifold, you can include some of that too.
qtbabe9876a9

qtbabe9876a9

Beginner2022-06-01Added 4 answers

Hint: Not only that. If you find a bounded trajectory then its closure is also an invariant set. (It can only be made the trajectory and fixed points). I suggest you try to run it through a numerical program so you get the feel of the system.

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