$L_{\alpha}(z) = \alpha z$ where $z$ is a complex number and $\alpha$ is a constant and is also complex.
How do I prove for $|\alpha|<1$ all orbits tend to a unique limit and how do I find this limit?
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1Here's a hint: Try to compute an explicit formula for the $p^{\text{th}}$ iterate, $L_{\alpha}^p(z)$. – Mark McClure May 21 '13 at 14:47