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## Homework Statement

suppose f and g are conjugate

show that if p is an attractive fixed point of f(x), then h(p) is an attractive fixed point of g(x).

## Homework Equations

f and g being conjugate means there exist continuous bijections h and h^-1 so that h(f(x)) = g(h(x))

a point p is an attractive fixed point of there exists an interval I = (p-a,p+a) such that for all x in I the iterates of f(x) tend to p as the number of iterations tends to infinity

## The Attempt at a Solution

so far I can show that if p is a fixed point of f then h(p) is a fixed point of g:

h(f(p)) = g(h(p)) and we know f(p) = p so simplify to get

h(p) = g(h(p)) and this part is now done.

Also, I know that if x is in I, then h(x) is in h(I)

what I want to show is that for all x in h(I), g

^{n}(x) -> h(p)

(that is, the iterates of x under g converge to h(p))

and thats as far as Ive gotten. How can I proceed?