Thread: Chaos Theory: period points

Hi, I have this question

Let f: (R is the set of real numbers) and let intersect the graph of the identity mapping id in just one point (call it p). How many points of period-1 does f have? In how many points does the graph of f intersect that of id?

I know that the point p is a fixed point of and I know that if f has a fixed point then it is also a fixed point of , so f can have at most one fixed point. But I just can't seem to get my head around this question.

Please help
Katy

Yes, if p is a point of period 1 for f, then it is a fixed point for f and so for . Thus, if has only one fixed point, then so does f. The only thing you seem to have left undone is the number of points in which the graph of f intersects the graph of the identity function. But if p lies on both y= f(x) and y= x, then y= f(p)= p and p is a fixed point. Since f has only one fixed point, in how many points can y= f(x) intersect y= x?

So it intersects only once? Is that right?

So is there no way that there can be no fixed points for f and a fixed point for ?