Iterative Systems of Difference Equations

kathrynag
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If one were to solve an iterative system, how would they do so. I'm studying them, and am wondering how to find fixed points?
For example, say I have x_{n+1}=x_{n}^{2} and was looking at fixed points how would I do so. I'm studying fixed points and attracting and repelling.
 
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Hi kathrynag! :smile:

(try using the X2 tag just above the Reply box :wink:)

At a fixed point, you can put xn = xn+1 …

in your example, the fixed points will be x = 0 or 1. :smile:
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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