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arXiv 1111.3720math.DS
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可和性意味着科莱-埃克曼几乎肯定

Summability implies Collet-Eckmann almost surely

Bing Gao, Weixiao Shen

摘要:

我们提供了一个著名的雅各布森定理的加强版本。考虑一个区间映射$f$满足可和性条件。对于一般的单参数映射族$f_t$与$f_0=f$,我们证明了$t=0$是一个Lebesgue密度点的参数集$f_t$满足收集Eckmann条件和强多项式递归条件。

英文摘要:

We provide a strengthened version of the famous Jakobson's theorem. Consider an interval map $f$ satisfying a summability condition. For a generic one-parameter family $f_t$ of maps with $f_0=f$, we prove that $t=0$ is a Lebesgue density point of the set of parameters for which $f_t$ satisfies both the Collect-Eckmann condition and a strong polynomial recurrence condition.

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