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

Hisa-Aki TANAKA; Shin'ichi OISHI; Atsushi OKADA

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

Hisa-Aki TANAKA, Shin'ichi OISHI, Atsushi OKADA

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.7 pp.1117-1120

Publication Date: 1993/07/25

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Type of Manuscript: Special Section LETTER (Special Section of Letters Selected from the 1993 IEICE Spring Conference)

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Hisa-Aki TANAKA, Shin'ichi OISHI, Atsushi OKADA, "Numerical Verification of Algebraic Non-integrability for High Dimensional Dynamical Systems" in IEICE TRANSACTIONS on Fundamentals, vol. E76-A, no. 7, pp. 1117-1120, July 1993, doi: .
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e76-a_7_1117/_p

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@ARTICLE{e76-a_7_1117,
author={Hisa-Aki TANAKA, Shin'ichi OISHI, Atsushi OKADA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Numerical Verification of Algebraic Non-integrability for High Dimensional Dynamical Systems},
year={1993},
volume={E76-A},
number={7},
pages={1117-1120},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={July},}

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TY - JOUR
TI - Numerical Verification of Algebraic Non-integrability for High Dimensional Dynamical Systems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1117
EP - 1120
AU - Hisa-Aki TANAKA
AU - Shin'ichi OISHI
AU - Atsushi OKADA
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E76-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 1993
AB - 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.
ER -