Rates of Divergence of Nonconventional Ergodic Averages
نویسنده
چکیده
We study the rate of growth of ergodic sums along a sequence (an) of times: SNf(x) = ∑ n≤N f(T nx). We characterize the maximal rate of growth and identify a number of sequences such as an = 2, along which the maximal rate of growth is achieved. We also return to Khintchine’s Strong Uniform Distribution Conjecture that the averages (1/N) ∑ n≤N f(nx mod 1) converge pointwise to ∫ f for integrable functions f , giving an elementary counterexample and proving that divergence occurs at the maximal rate.
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تاریخ انتشار 2004