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Dynamical Systems, Basin of Attraction Proof

  1. Sep 23, 2008 #1
    1. The problem statement, all variables and given/known data

    Suppose that f: I->I is a continuous and onto map on an interval I. Let x1 be an asymptotically stable periodic point of period k>=2. Show that Ws(f(x1))=f(Ws(x1))

    2. Relevant equations
    Ws(x), the basin of attraction of x1 is defined as {x: lim (n->infinity) f^n(x)=x1}. Note f^n is f(f(f(f(f(x), or f composed n times.

    3. The attempt at a solution

    I think that since x1 is a periodic point, so there is another k-period point I called x2 for which f(x1)=x2. So then the right side becomes the Basin of Attraction for x2. But I'm not sure how to describe the basin of attraction of x1 under f.
  2. jcsd
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