ON DYNAMICS OF SOME DIFFERENCE EQUATIONS

In present work we investigate the difference equations $x_{n+1}=f(x_{n}),\,\,n\geq0.$We consider the case when the function $f$ is power series. It is proved that under some condition to $f$the solution of difference equation asymptotically equivalent to $bn^{\alpha},\,\alpha>0,$ as $n\rightarrow \infty.$

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