Taylor series maps and their domain of convergence
作者:
Dan T. Abell,
Alex J. Dragt,
期刊:
AIP Conference Proceedings
(AIP Available online 1992)
卷期:
Volume 292,
issue 1
页码: 230-259
ISSN:0094-243X
年代: 1992
DOI:10.1063/1.45111
出版商: AIP
数据来源: AIP
摘要:
This paper tries to make clear what limits the validity of a Taylor series map, and how. We describe the concept of a transfer map and quote some theorems that justify not only their existence but also their advantages. Then, we describe the Taylor series representation for transfer maps. Following that, we attempt to elucidate some of the basic theorems from the theory of functions of one and several complex variables. This material forms the core of our understanding of what limits the domain of convergence of Taylor series maps. Lastly, we use the concrete example of a simple anharmonic oscillator to illustrate how the theorems from several complex variable theory affect the domain convergence of Taylor series maps. There we describe the singularities of the anharmonic oscillator in the complex planes of the initial conditions, show how they constrain our use of a Taylor series map, and then discuss our findings. (AIP)
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