数理解析研究所講究録
第 536 巻 1984 年 1-31

A SHORT HISTORY OF OUR COOPERATIVE SYMPOSIUMSAT THE RESEARCH INSTITUTE
FOR MATHEMATICAL SCIENCES OF KYOTO UNIVERSITY

Kenichi SHIRAIWA
Department of Mathematics
College of General Education
Nagoya University

謙一

白岩

名古屋大学

教養部

It has elapsed about ten years since we $tarted meeting for asymposium at the Research Institute for Mathemtical Sciences of Kyoto
University in order to develop the interdisciplinary research ondynamical systems and its related fields.

The first meeting was heldfrom July 7 to July 12 of 1975 and its aim was the study of dynamicalsystems on electrical circuits.

I organized the meeting with Y. Ueda ‘engineers gathered together.
cooperation.

About 20 mathematicians and electrical$s$

The following mathematicians gave a series of lectures

surveying the recent development of the theory of differentiable
dynamical systems:

H. Imanishi, K. Shiraiwa, G. Ikegami, S. Ichiraku,T. Nishimor , T. Okabe, S. Ma sumoto , M. Kurata, H. Matsue, T. Niwa,
$i$

$t$

K. Yamato, and M. Goto.
T. Matsumoto and T. Ito gave lectures on a general theory ofdynamical systems arising from electrical networks developed byR. Brayton, J. Moser, and S. Smale.

Furthermore, T. Matsumoto present-ed his recent works and many interesting problems.
Y. Ueda, H. Kawakami, and N. Akamatsu gave many interesting

results on the solutions of Duffing‘and digital computers.

$s$Equation by means of analogue

Many pictures of phase portraits, bifurcation

diagrams, and invariant sets of the Poincar\’e mappings which are now

called strange attractors were shown, and its relation to the theory of$/$$\sim’\cap$differentiable dynamical systems were discussed.

The proceedings ofthe symposium was published as the Kokyuroku No. 254(1975) of theResearch Institute for Mathematical Sciences of Kyoto University inJapanese.

The meeting was so fruitful that we decided to continue theproject.

The second and the third meetings were held from July 5 toJuly 8 of 1976 and from July 6 to July 9 of 1977 respectively on theThe organizer of the both meetings was Y. Ueda in cooper-same theme.

ation with me from mathematical point of view.
At the second meeting, S. Ichiraku, a mathematician, presented apaper answering a problem posed by T. Matsumoto at the first meeting.
This is the$f$

irst concrete work based on our proj ect.

Since then,many cooperative researches were performed by mathematicians, scientistsof the other fields, and engineers.
New contributors were as follows: (the second meeting) Y. Akamatsu,
T. Koike, T. Otsuki; (the third meeting) T. Tsuboi, T. Matsumura,K. Yano, A. Morimoto.

The proceedings of the second and the thirdmeetings are the Kokyuroku No. 284(1976) and No. 313(1977) respectively.
We took rest in 1978 and took a further step in 1979, $i.e$. we holdthe fourth meeting from July 11 to July 14 of 1979 on an extended theme.
The following topics were included:

Difference Equations Arising From

Economics by F. Nakaj ima, Oscillators of Many Degrees of Freedom by
M. Kuramitsu, Chaotic Behaviors in the Belousov-Zhabotinsky Reactions

by K. Tomita and I. Tsuda, and Chaos in Lorenz Equations by S. Ushiki.

Other new contributors were K. Sasano, N. Kakiuchi, A. Sannami,
A. Koriyama, and H. Matsuoka.

The proceeding is the Kokyuroku No. 370(1979).

The fifth meeting was held from July 14 to July 17 of 1980 and

its theme was ”Chaotic Phenomena in Deterministic Systems and Dynamical
System Theory\dagger ’.

The organizer of the fourth and fifth meetings wasY. Ueda cooperated with me.

New contributors were F. Takase, I. Ishii,

S. Oishi, Y. Okumura, T. Ushio, K. Hirai, M. Iwai, T. Kohda, M. Dateyama,T. Nagase, and N. Aoki.

The Kokyuroku No. 413(1981) is the proceedingof the fifth meeting.

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3The sixth and the seventh meetings were held from July 8 to July

11 of 1981 and from July 7 to July 10 of 1982 respectively on the fully
extended theme.

Both meetings were organized by G. Ikegami in cooper-ation with Y. Ueda.

Proceedings are the Kokyuroku No. 443(1981) andNo. 466(1982) respectively.

From 80 to 90 researchers gathered together

for each of these symposiums from various fields such as mathematics,physics, chemistry, biology, earth science, electric engineering, computer science, control theory, and other sciences and engineerings.

The new contributors were as follows: (the sixth meeting)
G. Seifert, H. Ogura, H. Yoshida, K. Murao, K. Hiraide, T. Toyoda,H. Daido, T. Shimada, Y. Katsuta, J. Matsuo, R. Kuwabara; (the seventhmeeting) Y. Kuramoto, S. Koga, M. Kitano, T. Yabusaki, T. Ogawa,K. Maginu, S. Sato, K. Naka, E. Hida, R. Ito, H. Igo, K. Sawada,M. Nakada.

The eighth meeting was held from July 6 to July 9 of 1983 on thetheme “Nonlinear Phenomena and Dynamical Systems”.
H. Kawakami in cooperation with me.
No. 506(1983).

The organizer wasThe proceedings is the Kokyuroku

The new contributors were as follows:

T. Kohyama, Y. Aizawa, Y. Togawa, N.

M. Komuro,Sait\^O, M. Yamagut , M. Hata,$i$

J. Kigami, M. Matsubara, H. Kokubu, H. Oka, N. Yamamoto.

The ninth meeting is also organized by H. Kawakami in cooperation
with me, and this is the proceedings of this symposium.
Now it becomes obvious that our project is successful.

We arevery grateful to the Research Institute for Mathematical Sciences forgiving us an opportunity of holding such fruitful symposiums.

We feelthat mathematicians, scientists, and engineers should cooperate in theresearch of dynamical systems.

Such cooperations are mutually advan-tageous for mathematicians, other scientists, and engineers.

I hopethat such cooperations are everlasting and fruitful for the advancementof sciences and engineerings.

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