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Apr 9, 2010 at 7:03 comment added Thorny You mean $\alpha$, if I understand you correctly. I am giving you a construction of an $\alpha$ for which the dynamical system exhibits an infinite $A$, so there is no modification. I assume there could be an explicit $\alpha$ given, something along the lines of $\sum 10^{-10^{k^2}}$ - as long as it can be approximated superexponentially, the set $A$ will be infinite for all $\delta>0$.
Apr 8, 2010 at 16:00 comment added Kaminoite The thing is that you can not modify the value $\delta$. The question states that it must be fixed.
Apr 8, 2010 at 14:48 history answered Thorny CC BY-SA 2.5