AI 中文总结
该研究针对奇异值缓慢逃逸至无穷的指数映射，构造了回复与非回复的例子，补充了相关学者的早期结果，还给出了奇异值逃逸速率任意慢的参数化例子。
AI 中文摘要
我们通过在指数族中给出两个奇异值“缓慢”逃逸至无穷的例子，证明指数映射可具有复杂的可测行为：其中一个是回复的（即每个正测度集都将无限次返回自身），另一个则是非回复的。这也补充了Lyubich、Rees、Urbański-Zdunik和Hemke的早期结果。我们还给出了一个奇异值以任意慢的速率逃逸至无穷的指数映射例子，这是Rempe结果的参数化类似物。
英文摘要
We show that exponential maps could have complicated measurable behaviours by giving two examples in the exponential family both with singular value escaping to infinity ``slowly", one of which is recurrent (in the sense that every positive measure set will return to itself infinitely many times), while the other is non-recurrent. This also complements earlier results of Lyubich, Rees, Urbański-Zdunik, and Hemke. We also give an example of exponential maps with singular value escaping to infinity arbitrarily slow, which is a parametric analog of a result of Rempe.
Comments13 pages; comments welcome
