指数图的扰动：非循环动力学

Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI:10.1007/s11854-024-0340-5

Magnus Aspenberg, Weiwei Cui

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引用次数: 0

摘要

我们研究了指数族中非循环参数的扰动。结果表明，此类参数集的勒贝格度量为零。这尤其意味着逃逸参数集的勒贝格度量为零，从而补充了邱晓华 1994 年的一个结果。此外，我们还证明了非循环参数可以用双曲参数近似。

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Perturbations of exponential maps: Non-recurrent dynamics

We study perturbations of non-recurrent parameters in the exponential family. It is shown that the set of such parameters has Lebesgue measure zero. This particularly implies that the set of escaping parameters has Lebesgue measure zero, which complements a result of Qiu from 1994. Moreover, we show that non-recurrent parameters can be approximated by hyperbolic ones.

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Journal d'Analyse Mathématique

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