Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.chronos.msu.ru/old/RREPORTS/koganov_induktornye.pdf Äàòà èçìåíåíèÿ: Sat Dec 14 13:12:32 2013 Äàòà èíäåêñèðîâàíèÿ: Fri Feb 28 11:54:42 2014 Êîäèðîâêà:

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- ; Web- http://www.chronos.msu.ru; koganow@niisi.msk.ru

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1.
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07-01-00101.


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, . . () - . , , . , , . , , , () . , . . ( ) , , , . . , , () . , ­ . . . , . . -

, . : , . . , . . , ­ . , , . . (), , . , . , - . , - , , . , . , . , . , , , -


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, : . . . , . : . . , , , . . . ( ) , , , , . , , , , . , . . , , , . . , . , .

, , . . , , . , , . . (, 2002). , . . , (, ) x , . , , . ( ), . , -. -


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( ) , . , ­ , ­ . , . , , , . , . , , . , . . . , . .. (1999) , , .. (1980). .. (1996; 1999) , , . , , . (1977), ­ .. (1980). , , .. (1977) (1988). .

2. ­
2.1. (-) T ITâ2T, [t,V]I, t ­ , V ­ t. [T,I] (-) T I , ( I(x) xT): 1. . : [t,V]ItV. 2. . [t,V]I [t',U]I t'V, [t,VU]I. , (, ) . I T. 2.1. J [T,I] . I=spase(J). 2.2. () ­ IT2. ­ I2T. (, 1996; 1999). [x,V]I, V ­ xT. [x,V]I, V ­ n- xT. 2.1. 2.3. , , ( ). , ­ . .


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, , , (, 1996; 1999). , . 2.2. MT M , M ( M). (-) M=M\M. t=V | [t,V]I tT . M=t | tM. t=V | [t,V]I. 2.4. - , - 2.2, . , [x,V']I, V ­ xT, V' ­ . V' V. 2.3. [T,I] [T,I'], [t,V]I' [t,W]I', WV. [T,I] [T,I'] , . 2.5. (., , .. , 1977). I'I, I I', . f g T t (. . f(t)=g(t)tV [t,V]I), .

3.
3.1. [T,I] P:XTYT, P:x(:t)|y(t)=defP(x(:t),t)=P(x,t), X Y ­ x(t) y(t) () tT; x(:M) ­ (-

) MT; P(x,t) ­ . 3.2. - A:XTâYTYT, A:(x(:V), y(:V),t)|y(t)=A(x,y,[t,V]), [t,V]I ­ I. , , . P A, t x. 3.1. . , , , , . , , . , (123...), , j ((j­k)(j­k+1)...(j)) {(j­k)} {(j­k+1)...(j)}. yj=A(xj­k,...,xj;yj­k), A ­ k . [t,V]I' t loc(t), y=A(x,y,loc(t)), . 3.3. , V V=VV. f(:m), mT : f(:m)f'(:u)=f"(:mu)=f(:m) | f'(:u\m). , f(:mu)=f"(:mu). . f(t) f(:{t}).


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3.1. [T,I] , . . . . VVV. , V\(VV)=U [t,V]. , . X=Y={0;1}. t"U. P(x,t')=0 t't x(:T); P(x,t)=x(t"). A S s(t)=A(x(:V),s(:V),t) x(t"), t"VV. , P. . P ­ X Y. S x(:t),tT. s(t)=x(:t). [t,V]I s(t)=x(:V)x(:V)=x(:V)s(:V)=defA(x,s,[t,V]), . . , P(x,t)=P(x(:t),t)=P(s(t),t), . 3.4. , x(:T) y(:T) y(:T). , . - , . - [T,I] , JI, I . ( loc(t)J ).

. J ( ) . . 3.5. [T,I] [t1,V1]I, [t2,V2]I,..., ti+1Vi;i=1,... 3.6. {0;1}, : (3.1) y(t)=max{y(t') | t'loc(t)}. 3.2. , ( , ). . . , . W=Vi | i=1,... y(:T) y'(:T). y'0; y(:T)0 tT

(3.1). Vi. , W T, . , y(:Vi)=1. . , loc(t) T T T, . , . WI. , , . TWl. , .


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W2. , W3, W4,.... tT . 3.1. ( ). , (3.1) . , I'I , ( ) loc(t)I'. 3.2. - , JI, I I', 3.2. 3.3. , . 3.4. , , ­ (, 1996; 1999). Rn 2, . . , , . 3.7. , , , . , J I ( 3.4). 3.3. : {loc(t) | tT} t ( tI)

t't,t'=tn. , , . . . P y(t)= =A(x,y,loc(t)). , y : Z={z=y(:m) | mT}. z(t)=y(:t)=Uy(:t')|t'loc(t). , y(:T) . t t . tT, {(t',z(t')) | t'loc(t)}=z(: loc(t)) x(:loc(t)) y(t)=A(x(:t), y(:),t), P(x,t). , z P. . , loc(t) t t't. , , [ti,Vi]I,i=1,..., t=t1. P . , . I', . , Z ( ) z(t)=A(z(loc(t)),t) , P(t) | y(:t)=y(t)=f(z(t)). z(:T) y(:T), y(t')=0, z'(:T) y'(:T),y'(t")=y(t") t"t', y'(t')=1. W=UVi | i=1,..., Q={t" | loc(t")W}. z"(:Q)=z'(:Q), z"(T\Q)= =z(:T\Q). W, z z" y(:T), t'W. y'(: T\{t'})=y(: T\{t'})=0. f(z(t))=0, f(z"(t))=1, z=A. 3.5. , , , , -


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. , . 3.2. , , , . , . , . , , . 3.4. y(t)= =A(x,y,loc(t)), y(:loc(t))=A'(x,y,loc(t))=A'(x(:loc(t)), y(: loc(t))) A'. 3.1. t'V [t,V]I [t',W]I , WV. . : t'V W' u'=W'\V. W=UW' | [t',W']I,W'V. [t',W]I. u' W u. , u V, W, uW. , uV, . , 3.4, A'(x(:loc(t)),y(:loc(t)))=y(:loc(t))UA(x,y,loc(t')) | t'loc(t)&loc(t')loc(t).

4.
4.1. p, S, p:SS, p2=p. , -

(., , , 1988). 4.1. , , . . [T,I] y(t)=A(x,y,loc(t)), tT, y(t)Y, x(t)X. x(:T) . y(:T) y(:T), A|y(:T). y'(:T). py'=A|y'(:T)=y(:T). y'(:T)=y(:T). p2y'=py=A|y(:T)= =A|y'(:T)=y(:T)=py'. y' p. 4.2. p:SS ( S) ( k) Hp L(S,k) f:Sk, : Hpf(s)=f(ps), s S. 4.2. : a) p q S Hpq=HqHp. b) p Hp ­ . c) p WS JW ­ W, JWHp, , p L(W,k). d) p ­ , sS (, ) b(s)={s'|ps'=s}, pS ­ p. Hp ­ , f(s')=f(s) s'b(s). .


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4.1. , , . , , . , , . , ­ . . 4.2. () () (. 1).
. 1.

( ). , . 5.1. aut Rc[1] ­ R1; aut Rc[2]=aut Rc[1]âaut Rc[1]âS2:R2, S2 ­ x2, . . ; aut Rc[n]=Lor[n] R+:Rn, n3, R+ ­ Rn. 5.2. aut Rb[1] ­ R1, . . aut Rb[1]=aut Rc[1]âS2:R1; aut Rb[2]=aut Rc[1]âaut Rc[1]âS2âS2:R2, S2âS2 ­ R2 ­ ; aut Rb[n]=Lor[n]âRh:Rn n>3, Rh ­ . Lor[n] ­ . , 2. . aut Rb[n] aut Rc[n] x1, . . n=1. ­ « »: , ­ ( ) . ­ , . ( ) , . n=2. ­ ­ .

( ( ) ) ( ) ( )

5.
5.1. Rc[n] Rn, y , x1,...,xn 0(x1­y1)2­(x2­y2)2­...­(xn­yn)2, 0x1H, H>0. |x1|H, Rb[n]. ; , , aut Rb[n] aut Rc[n]. (, 1996), Rb[n] Rc[n] Lor[n] Rn, , , ­ .


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, ( ) . , (0,0) e, t. . U ­ , U(x,y)=U(xe+yt)=U(0,0)+V(x)e+W(y)t, V, W ­ , U(x,y)=U(xe+yt)=U(0,0)+V(x)t+W(y)e, V, W ­ . 5.1. n=3. , , . . , . . - ­ , . - ­ , -. - ­ , -. - ­ , -. - ­ , -. - ­ -. - ­ , -. , -, - -. 5.1. Rn. . , r(1),r(2),... r. - (K(i)|i=1,...) g(1),g(2),... H(1),H(2),..., r(j), ji K(i). r. u - K(1),K(2),... - {uK(i)|i=1,...} ur. ur(j),ji, - uK(i). , 5.1 .

5.2. - -. . , -, -. - L. -. r L -, L . , L. , . , -, -, 5.2 . 5.3. - - - - . - - ( , ). . - -. , () - . - -, ( ). -, , . . - -. - , -. - B r - L, B K. - -, L. - (K(i)|i=1,...), g(1),g(2),... r L. K(i) r i 0. K(i) B , - . i ­ , B . 5.1 B K(i), --


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, -. , - - . 5.2 - -, , ­ -, - ( - 5.2), . . -. - -, - . , , . ( 5.1) , . -, -. - -. 5.1 - -. 5.3 . 5.4. - -. . - 5.3. - - -, . -, - , , , ­ -, -. . , -. - - -, - . 5.4 . . - A - B. Rn x=a+b, a=a(x)A, b=b(x)B. Rn aA, bB x(t)=at+bt, t ­ . t x , at bt, tatb. u ( 5.4) tuatub. ,

ua=v+w; ub=f+g, v, fA; w, gB; ux(t)=t(v+f)+t(w+g), , , . . n=3 . n>3. , n=3 . , ­ . , n=m. n=m+1. . : Rn=L{e0,e1,...,en}, e0 ­ -. : Rn=L{e0,e1,...,em}+L{e0,e1,...,em­2,en}. ­ m- . ( ) u, , , u . u . lRn, e1,e2 , lL{e0,e1,e2}, , , lL{e0,e1,...,em}. e0,v,w­v, w v ­ l. ul . .

6.
6.1. M [T,I] x, M. M (6.1) Lim(M|I)={x|[x,U]IUM}. 6.2. T I J, J I, J I: MT Lim(M|I)Lim(M|J). (6.2) 6.3. - [T,I] - r:T2Rn, n ­ :


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r(x,y)=(r1(x,y),...,rn(x,y)) x,yT, ri(x,y)R. (6.3) - - r (6.4) - z x (6.5) Sr(x,z)={y| |r|(x,y)z}. Ir , : (6.6) Ir=spase{[x,Sr(x,z)] | xT; z>0}. r(x,x)=0 Ir I (6.2). 6.1. (6.4) - . . 6.4. Q M F T, I, Q:FâIM, . f,gF, VI(x) f(y)=g(y) yV, Q(f,W)=Q(g,W) WI(x). (6.7) , Q(f,W)=Q(f,W') W,W'I(x), xT. f x, () , Q(f)(x). , -, . . 6.5. [T,I], [P,J] q:IP. , yP q xT, WI(x) (6.8) yLim({q(x,V)|VI(x),VW} J).

: yLim(q)_I(x) y=lim(q)_I(x), . 6.1. (6.7) D. , P=M J={[y,{y}]J|yM}. Q(f)(x)=lim(Q(f,.))_I(x). 6.2. [T,I] xT I(x)I(x), q 6.5 (6.9) q(x, I(x))=lim(q)_I(x) (6.8) W=I(x). V=W, . . 6.2 xT (6.10) Q(f)(x)=Q(f,I(x)). 6.6. , [T,I] n- - r L, . f:TK, K ­ , [x,V]I n- B=B(x,V), (6.11) . 6.2. , : (6.12) NV{.} V: (6.13) [T,I;r,N,K]. B.


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6.7. (-) f x [T,I;r,N,K] (6.14) - ( , ) , (6.14). 6.8. : (6.15) 6.3. K , (6.15) ­ . . (6.15) , B(x,V). 6.1. f - x, VI(x) NV{f(.)­f(x)­Br(x,.)}NV{f(.)­f(x)­f'(x)r(x,.)}+N{Ar(x,.)}, (6.16) (6.17) AKn, lim(||A||)_I(x)=0. . (6.14). , a>0 WI(x) , VW ||B(x,V)­f'(x)||
. , - . {f'(x)} . B1,B2{f'(x)}, B1B2. J1,J2I(x), lim(B(x,V))_Ji=Bi, i=1,2. , |B1­B2|=O(||r{x,.}||V), NV{f(.)­f(x)­B(x,V)r(x,.)}=O(||r{x,.}||V). , (6.19). 6.2. f(.) x f*(x), : (6.20) NV{f(.)­f(x)­f*(x)r(x,.)}=o(||r{x,.}||V). . (6.19) NV{f(.)­f(x)­Br(x,.)}=o(||r{x,.}||V). 6.1 NV{f(.)­f(x)­Br(x,.)}=NV{f(.)­f(x)­f*(x)r(x,.)}=o(||r{x,.}||V). (6.20). 6.4. 6.2 f '(x)= =B(x,I(x)). 6.7 (6.9). 6.4. 6.1 - f/x=f'+o(x). F(x+x)=f'x+o(x) 6.2. 6.4 . 6.10. , (1996), Rc[1]=[R,I+,r], R=(­;), I+={[x,[x­u;x]]I+ | xR, u>0}, r(x,y)=x­y. 6.5. (, (, 1999)). 6.5. (6.12) :

( .)


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6.6. f R tR Df=U, D ­ , U ­ , . f(.|P,t0), t0 ­ R, P ­ , . Rc[1] Q={(Pi,ti)}, tiR, ti


V



.. . ., 1977. . . . . 4. .: , 1977. 415 . .. Processes and Automorphisms on Inductor Spaces. Russian Journal Mathematic Physic. Vol. 4. 3. 1996. P. 315­339. .. // (, , , ). .: , 1999. . 182­189. .. , // (, , , ). .: , 1999. . 119­181. .. // . . . . 9. . 2. .: : R&C-Dynamica, 2002. . 373­384. .. . .: , 1980. 149 . , «». .: , 1988. . 223.