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fixed point iteration

Here's a general link about iterated functions: Iterated function - Wikipedia, the free encyclopedia

Consider f(x)=x^{2}-2 for x in the closed interval [-2,2]. Let f^{n}be the nth iterate of f. Also let a be in [-2,2]; define the sequence x_{n}by x_{0}= a and x_{n+1}= f(x_{n}).

1. Is there a with x_{n}unequal to -1 for all n, but x_{n}converges to -1?

2. Is the set D={a : x_{n}= 2 for some n} dense in [-2,2]?

3. Are there orbits of f of arbitrary length?

I know very little about iterated function theory, so maybe these are "easy" questions, but ??