Find $K, \Omega \in \mathbb{R}$ such that the circle map $\theta_{n-1} = [\theta_n + \Omega + \dfrac{K}{2\pi}\sin(2\pi \theta_n)]\quad(\mod 1)$ has a fixed point and a period $3$ orbit.
I was reading through this document https://www.physics.drexel.edu/~bob/PHYS750_NLD/ch7.pdf to try to get a better understanding of circle maps. And I was wondering if one can find these parameters in some obvious way that I'm just not thinking of?
If somebody has some suggestion as to where I can find the information I need or if somebody could please explain it to me that would be great!
Thanks!