$\alpha$-连分数熵的调整与平台
动力系统
2015-06-03 v2
摘要
已知 -连分数变换的熵 在闭的、全不连通集 之外是局部单调的。我们将利用 分形结构的显式描述来研究函数 图像所展示的自相似性。最后，我们完全刻画了该图像中出现的平台，并对局部单调行为进行了分类。
关键词
引用
@article{arxiv.1111.2554,
title = {Tuning and plateaux for the entropy of $\alpha$-continued fractions},
author = {Carlo Carminati and Giulio Tiozzo},
journal= {arXiv preprint arXiv:1111.2554},
year = {2015}
}
备注
20 pages, 2 figures. This version has been considerably expanded, and contains a new result (Theorem 3) classifying local behaviour of the entropy. We have also added several statements and proofs in order to avoid external references. Last but not least, we added an appendix which explains how the techniques we use are derived from Douady-Hubbard tuning for quadratic polynomials