Numerical Verification of Algebraic Non-integrability for High Dimensional Dynamical Systems

Hisa-Aki TANAKA  Shin'ichi OISHI  Atsushi OKADA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A   No.7   pp.1117-1120
Publication Date: 1993/07/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section of Letters Selected from the 1993 IEICE Spring Conference)
Category: 
Keyword: 
singular point analysis,  high dimensional dynamical system,  self-validating numerics,  

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Summary: 
The singular point analysis, such as the Painlev test and Yoshida's test, is a computational method and has been implemented in a symbolic computational manner. But, in applying the singular point analysis to high dimensional and/or "complex" dynamical systems, we face with some computational difficulties. To cope with these difficulties, we propose a new numerical technique of the singular point analysis with the aid of the self-validating numerics. Using this technique, the singular point analysis can now be applicable to a wide class of high dimensional and/or "complex" dynamical systems, and in many cases dynamical properties such as the algebraic non-integrability can be proven for such systems.