Find an example of a $C^1$ diffeomorphism with a non-hyperbolic fixed point which is an accumulation of other fixed points.
A fixed point which is not an hyperbolic point must satisfy that $$f^n(p)=1,$$ and for $C^1$, it must hence give that $$f'(p)=1.$$
Let is place a fix point at $x=\pi/2$, and let that give $f'(p)=1\implies f'(\pi/2)=1$. Such a function is $f'(x)=\sin{x}$. We integrate and obtain $f(x)=\cos{x}+C$.
But here we have a C, and I don't know how that affects the results, being undefined.
Any suggestions appreciated