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Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x
Ivars Wrote:

This can be easier expressed as Wink


That seems indeed true. Basicly it has to do with that is a (the only) fixed point of . Proof:

this can not be satisfied for as has no fixed point. So we consider the case , which is equivalent to which is by your definition .

However that fixed point is repelling , thatswhy does not converge. On the other hand the iterated value is always thrown back into the negative domain by for positve . And there it oscillates around the fixed point until it is again repelled into the positive domain. So most time it is oscillating around , thatswhy the average is just this.

Messages In This Thread
RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by bo198214 - 03/27/2008, 09:29 AM

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