Special functions created by Borel-Laplace transform of Hénon map

Q3 Mathematics

Electronic Research Announcements in Mathematical Sciences Pub Date : 2011-01-01 DOI:10.3934/ERA.2011.18.1

C. Matsuoka, K. Hiraide

引用次数: 3

Abstract

We present a novel class of functions that can describe the stable and unstable manifolds of the Henon map. We propose an algorithm to construct these functions by using the Borel-Laplace transform. Neither linearization nor perturbation is applied in the construction, and the obtained functions are exact solutions of the Henon map. We also show that it is possible to depict the chaotic attractor of the map by using one of these functions without explicitly using the properties of the attractor.

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由hsamnon映射的Borel-Laplace变换生成的特殊函数

我们提出了一类新的函数，可以描述Henon映射的稳定流形和不稳定流形。我们提出了一种利用Borel-Laplace变换来构造这些函数的算法。在构造过程中既不采用线性化，也不采用微扰，得到的函数是Henon映射的精确解。我们还证明了在不显式地使用吸引子的性质的情况下，用这些函数之一来描述映射的混沌吸引子是可能的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Research Announcements in Mathematical Sciences 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication. ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007