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arXiv math/0411371math.DSmath.FA
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应用于非线性动力学的多尺度理论和小波方法

Methods from multiscale theory and wavelets applied to non-linear dynamics

Dorin E. Dutkay, Palle E. T. Jorgensen

备注：
survey. v2: We have polished the writing and corrected some of the cross references and citations; and v2 has an acknowledgment paragraph added. Moreover, the ms has been converted to Birkhauser/OT style files. v3: added discussion of general themes of operator theory and how they complement the particular structure arising from multiscale theory, p. 22; regularized subsection numbering throughout; corrected some misspellings
发表信息：
Wavelets, Multiscale Systems and Hypercomplex Analysis (D. Alpay, ed.), Oper. Theory Adv. Appl., vol. 167, BirkhÃ?user, Boston, 2006, pp. 87--126
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摘要：

我们将展示如何从信号处理，多尺度理论和小波的基本思想可能被应用到非线性动力学。动力学中的问题包括迭代函数系统（IFS）、基于替换的动力系统（如建立在一个复变数的有理函数和相应的朱利亚集上的离散系统）以及符号动力学中的子移位的状态空间。我们的论文旨在激发和调查我们最近在这一领域的研究成果。因此，我们省略了一些证明，而是增加了一些直观的想法，我们希望这将使这个问题更容易为研究人员在运营商理论和系统理论。

英文摘要：

We show how fundamental ideas from signal processing, multiscale theory and wavelets may be applied to non-linear dynamics. The problems from dynamics include iterated function systems (IFS), dynamical systems based on substitution such as the discrete systems built on rational functions of one complex variable and the corresponding Julia sets, and state spaces of subshifts in symbolic dynamics. Our paper serves to motivate and survey our recent results in this general area. Hence we leave out some proofs, but instead add a number of intuitive ideas which we hope will make the subject more accessible to researchers in operator theory and systems theory.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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