Dynamical Systems

修し 7 _翻 塗

隊 爵

}

曽 数理解析研究所講究録

439

Random Systems and

Dynamical Systems

禁帯ムフ帰

3

56.22 2) t3

, C C kC!

歓薪図書室

ダ _マ ˆ

9 _つ汝

京都大学数理解析研究所

1981

10

Random

RIMS

Systems

Ko le ycL 7t. u le (L 4 39

and Dynamica1 Systems

ff Iys ¿ } ¡L t ￥ 5

284 1 430

pa g

;Ek 3gl fi4 in M fiM

September, l981

Research Xnstitute for Mathematical Sciences

Kyoto University, Kyoto, Japan

Random

R.I.M.S. Symposium

on

Systems and Dynamical Systems

l.

2.

3.

4.

5.

January 7-9, l981

Contents

Preface..eee...e...t...el H. Totoki

RIMS, Kyoto University

Similarity and Universality of Turbulence...···.·.3 T. Tatsumi

Department of Physics Kyoto University

Random Walks and Some Problems concerning Lorentz Gas....6

Landau Znstitute for [Pheoretical

Physics

Academy of Science USSR

Random Schr6dinger Operators...

e

.

e

e

l8

Department of Mathematics Kyoto University

On the St]puctuipe of the Set of Gibbs States fo]p the

2-dimensional Ising Ferromagnet...e.e····.···e····.···.·28 Y. Higuchi

Department of Mathematics Kobe University

-i-

6.

7.

8.

9.

]-Oe

ZLe

l2.

Soliton Equations as Dynamieal Systems on a !nfinite

Dimensional Grassmann IYIanifoids. · e.et.e.e.ee. · ..e.ee. · . · 30

M. Sato

RIMS, Kyoto University On Saddie-·connection Curves of Analytic Dynamical

SYSteMS ··· . · e.. ··· . ··· e ·· e · 47

S. Ushiki

Department of Mathematics Kyoto University

Chaos in One-

dimensionaZ DynamicaZ Systems....

.

..

..

54

Department of Mathematies Tsuda ColZege

Statistieal Properties of the Foyeed ZJorentz Chaos

—- Synergetie Approach to the System rdentification –..63

Department of Physics Kyoto University Outer Conjugaey Problem of Orbit Preserving

Transformations ... · ... · . · ...e. · 89

Cr. Hamaehi

Depa]?tment of Mathematies CoZiege of General Edueation Kyushu University

Reeent Development of Differentiable Dynamicai Systems

in Japan ... · .... · ...96

K. Shi!}aiwa

Department of Mathematies College of Geneyal Education Nagoya University

The Onsager-Maehiup Functions for Diffusion Processes..118

Department of Mathematics Kyoto University

”t ii -

13 ·

l4.

15 ·

Spitzer’s Markov Chains of the Hammerstein !Vype

On Some Properties of a Characterization of the

Speeification, Stability Group Automorphisms

and Non-linear rntegral Equations eeeeee-ee)e-eeee-e”eeeeeeeeee123 M. Miyamoto

Department of Mathematies

University Kyoto

Yoshida College,

Minimal Mow — A Topological

Strict Ergodicity —- ...128

z. rshii

Department of Mathemat±es

Faeulty of Scienee and Technoiogy Keio University

and rnvariant Measure for

...e.e.e...13Ll

M. Komuyo

Department of Mathematies Tokyo Metropolitan University

- iii -’

1

Preface

This volume of the Series ”RZMS Kokyuroku” (RZMS Seminar Reports) is the (informal) Proceedings of the Symposium on

”Random Systems and Dynamical Systems”, which was held at

University, from January 7 td 9, 1981. This Symposium was held on the occasion of the visit of Professor Ya. G. Sinai

(Landau Znstitute for Theoretical Physics in Moscow) to Japan (mainly Kyoto) during the period from January 4 to February 2,

198i.

Zn the Symposium eleven one-hour lectures and five 30–

minutes lectures were delivered. The contributions are arranged

in this Proceedings according to the order in which the lectures were given in the Symposium, except two lectures given by

Professor Sinai which are not included in this Proceedings.

More than 130 mathematicians and physicists participated in the Symposium.

Professor Sinai gave three lectures with the following titles:

1) Decay of correlations in dynamical systems.

2) New examples of phase transition in lattice systems

and generalized contour models.

3) Expository talk about recent results in dynamical

systems and statistical mechanics.

The first lecture is more or less contained in the

2

The second lecture is more or less contained in his book

”Rigorous Results in the Theory of Phase Transitions” (Russian,

Nauka, l980, Chapter 2; English transiation will be published

We would like to express our thanks to Professor Sinai for

his excellent lectures and his suggestive eomments on every lecture in the Symposium.

H. Totoki