AMERICAN MATHEMATICA L SOCIET Y TRANSLATIONS

Series 2

Volume 13 7

Fourteen Papers Translated from the Russian

by

V. I . Arnol' d S. D . Berma n K. Buzash i T. Donche v K. M . Efimo v I. I . Gikhma n S. G. Gindiki n M. I . Kanovic h A. A . Kirillo v

Yu. I . Mani n V. G . Maz'y a Yu. A . Nereti n A. A . Panchishki n Bl. Sendo v Ya. G . Sina i Vu Ki m Tua n E. B. Vinber g S. B . Yakubovic h

AMERICAN MATHEMATICA L SOCIET Y PROVIDENCE, RHOD E ISLAN D

http://dx.doi.org/10.1090/trans2/137

Translation edite d b y BE N SILVER

1980 Mathematics Subject Classification (198 5 Revision). Primar y 11FXX , 14H15 , 15-02 , 17A70 ,

17B05, 20-02 , 20C07 , 20G30 , 22EXX , 31B30 , 41A17 , 44A15 , 53A20 , 58A50 , 60GXX , 60H05 ,

68M10, 68Q10 , 76W05 ; Secondary 11S80 , 14MXX , 20C32 , 32G15 , 53C65 , 58F05 , 65D05 ,

70H20, 81E13 .

Library o f Congres s Cataloging-in-Publicatio n Dat a

Fourteen paper s translate d fro m th e Russian .

(American Mathematica l Societ y translations ; ser . 2 , v . 137 ) "Translation edite d b y Be n Silver"-T.p . verso . 1. Mathematics-Collecte d works-Translation s fro m Russian . I . Arnol'd , V . I . (Vladimi r

Igorevich), 1937 - . II . Silver , Ben . III . Series . QA3.A572 ser . 2 , vol . 13 7 510 s [510 ] 87-1752 6 ISBN 0-8218-3113- 5 (alk . paper )

COPYING AN D REPRINTING . Individua l reader s o f thi s publication , an d nonprofi t libraries actin g fo r them , ar e permitte d t o mak e fai r us e o f th e material , suc h a s t o cop y a n article fo r us e i n teachin g o r research . Permissio n i s grante d t o quot e brie f passage s fro m this publicatio n i n reviews , provide d th e customar y acknowledgmen t o f th e sourc e i s given .

Republication, systemati c copying , o r multipl e reproductio n o f air y materia l i n thi s publication (includin g abstracts ) i s permitte d onl y unde r licens e fro m th e America n Math -ematical Society . Request s fo r suc h permissio n shoul d b e addresse d t o th e Executiv e Director, America n Mathematica l Society , P.O . Bo x 6248 , ^Providence, Rhod e Islan d 02940 .

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Contents

A. A . Panchishkin , Loca l measure s correspondin g t o Eule r product s i n number fields 1

E. B . Vinberg , Effectiv e invarian t theor y 1 5 A. A . Kirillo v an d Yu . A . Neretin , Th e variet y A n o f n-dimensiona l Li e

algebra structure s 2 1 S. D . Berma n an d K . Buzash i [Buzasi] , O n representation s o f a grou p

containing a n infinit e cycli c subgrou p o f finite inde x 3 1 A. A. Kirillov, The orbit method and representations o f infinite-dimensiona l

Lie group s 3 7 V. G . Maz'y a an d T . Donchev , O n Wiene r regularit y a t a boundary poin t

for a polyharmonic operato r 5 3 Bl. Sendov , A modified Steklo v functio n 5 7 Vu Ki m Tua n an d S . B . Yakubovich , Th e Kontorovich-Lebede v integra l

transformation i n a ne w clas s o f functions 6 1

S. G . Gindikin , Hamiltonia n familie s o f rationa l curve s 6 7 I. I . Gikhman , O n a formul a fo r differentiatin g a stochasti c integra l wit h

respect t o a paramete r 7 7 Yu. I . Manin , Grassmannian s an d flags i n supergeometr y 8 7

K. M . Efimo v an d Ya . G . Sinai , Hydrodynami c mode s fo r a Lorent z ga s

with a periodi c configuratio n o f scatterer s 10 1 M. I . Kanovich , Complexit y o f hierarchical network s o f finite automat a 11 3 V. I . Arnol'd , O n th e evolutio n o f a magneti c field unde r th e actio n o f

transport an d diffusio n 11 9

Russian Contents *

A. A. riaHHHiiiKHH , JloKajibHbi e Mepbi , oTBenaiomHe 3HJiepoBCKH M

npoH3BeAeHHHM B HHCjioBbix nojiax , «Ajire6pa» . C6OPHH K pa6oT ,

nocBflin,. 90-JieTHK ) co AH A po CA - 0 . K) . IllMHATa , M3A-B O MTY,

MocKBa, 1982 , CTp. 119-13 7

3 . B . BHH6epr, 9<})(J3eKTHBHat f Teopn a HHBapnaHTOB , «Ajire6pa». C6OPHH K

pa6oT, nocBHni . 90-JieTHK ) co AH A poacA - 0 . K) . IllMHATa , M3A-B O MTY,

MocKBa, CTp . 27-3 3

A. A. KHPHJIJIO B H K). A. HepeTHH , M.Horoo6pa3He A n CTpyKTy p n-MepHbi x

ajire6p JIH , «HeKOTopbi e Bonpocb i coBpeMeHHor o aHajiH3a» , M3A-B O

MTY, MocKBa, 1984 , CTp. 41-5 6

C. J\. BepMaH H K. By3auiH , 0 npeACTaBJieHH^ x rpynnbi , coAep>Kain;e H

6ecKOHeHHyio iiHKjiHHecKyi o noArpynn y KOHenHor o HHAeKca , Publ .

Math. Dubrece n 2 9 (1982) , no . 1-2 , 162-17 0

A. A. KHPHJIJIOB , MCTO A op6n T H npeACTaBjieHHH 6ecKOHenHOMepHbi x rpyn n

JIH, TeoMeTpH H H TonoJiorna B rjio6ajibHbix HejiHHeHHbi x 3aAanax ,

M3A-BO BopoHe^ccK. Toe . YH-Ta , BOPOHOK , 1984 , CTp. 49-6 7

B. T . Ma3bf l H T. JXonneB, 0 peryjiapHocT H n o BnHep y rpaHHHHO H TOHK H

AJifl nojiHrapMOHHHecKor o onepaTopa , OKJiaA^ i BojirapcK . AicaA -

HayK, T . 36 (1983) , JNb . 2, 177-17 9

BJI. CeHAOB , MoAH^HUHpoBaHHaa (fcyHKijHi i CTeKjioBa , oKJiaA W BojirapcK .

AicaA. HayK , T . 3 6 (1983) , JNb . 3, 315-31 7

By KH M Tya H H C . B. HKV6OBHH , MHTerpajibHo e npeo6pa30BaHH e

KoHTopoBHHa-JIe6eAeBa B HOBOM KJiacc e (})yHKii,HH, XtoKJiaAbi AH BCCP,

T. 29 , JNb. 1 (1985), CTp . 11-1 4

*The America n Mathematica l Societ y schem e fo r transliteratio n o f Cyrilli c ma y b e found a t th e en d o f inde x issue s o f Mathematical Reviews.

IV

CONTENTS v

C. T . THHAHKHH , TaMMJIbTOHOBb l CeMeftCTB a paU,HOHaJIbHbI X KpHBblX ,

«HeKOTopbie Bonpocb i coBpeMeHHor o aHa;iH3a» , M3A-B O MTY, MocKBa ,

1984, cTp . 22-3 4

M. 14. THXMaH, 06 OAHO K (J)opMyji e AHCJxJDepemiHpoBaHH H CTOxacTHHecKor o

HHTerpajia n o napaMeTpbi , TeopH H cjiynaftHbi x npoueccoB , JNb . 10,

KneB, 1982 , CTp. 6-1 3

K). M. MaHHH, TpaccMaHMaHbi H (JmarH B cynepreoMeTpnH, «HeKOTopbi e

Bonpocbi coBpeMeHHor o aHajiH3a» , I43A-B O MTY, MocKBa , 1984 , CTp.

83-101

K. M. E({)HMO B H 51 . T. CMHafi , rHApoAHHaMHHecKHe MOAb i RJIX. ra3 a Jlopemj a

c nepnoAHHecKof t KOH(J)HrypaiiHef t paccenBaTejieK , «HeKOTopbi e

Bonpocbi coBpeMeHHor o aHajiH3a» , M3A-B O MTY, MocKBa , 1984 , CTp.

102-119

M. 14 . KaHOBHH, Cjio^KHocTb HepapxHHecKH x ceTe a M 3 KOHenHbi x

aBTOMaTOB, «MHoronj;aroBbie, AH(j)(})epeHu,HajibHbie , 6ecKoajiHU,MOHHbi e

H KoonepaTHBHbi e Hrpbi» , I43A-B O KajiHHHHCKoro Toe . YH-Ta ,

KajiMHHH, 1983 , CTp. 71-7 8

B. 14 . ApHOJibA, 0 6 3BOJIK)I;H H MarHHTHor o noji n no A AeftCTBHeM nepeHOc a H

AH(J)(})y3HH, «HeKOTopbie Bonpocb i coBpeMeHHor o aHajiH3a» , I43A-B O

MTY, MocKBa , 1984 , CTp. 8-2 1

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