
\vspace{0.5cm}
\noindent
{\bf 4. $B1?F0J}Dx<0$N3,?t9_2<(B(reduction)}

$B$3$NO@J8$G$O!"(B$m_1$$B$,Bg$-$/!"(B$m_2$$B$,>.$5$/!"(B$m_3$$B$,$5$i$K>.$5$$>l9g$K@)8B$7!"$^$?(B$m_1$$B$H(B$m_2$$B$N1?F0$,1_50F;$K6a$$>l9g$K@)8B$9$k!%$3$N$h$&$K$9$l$P!"%a%k%K%3%UK!$N$h$&$J$$$/$D$+$N@]F05;=Q$,;H$($k!%$3$N@a$G$OJ?LL;0BNLdBj$N1?F0J}Dx<0$r3,?t9_2<$7$F3F<o@]F0$,I>2A$G$-$k$h$&$K$9$k!%(B

$B$b$C$HE,Ev$J1?F0J}Dx<0$rF@$k$?$a$K!"$O$8$a$K?7$7$$JQ?t$r$$$/$D$+F3F~$9$k!%(B
$$ \begin{array}{ll}
 s = e^{i \theta}, & z = r e^{i \phi},
   \end{array}           
$$
$B$H$*$/!%$3$3$G(B$\theta,r,$$B$*$h$S(B$\phi$$B$O<B?t$G$"$k!%0lHL@-$r<:$&$3$H$J$/(B$\mu = m_1 + m_2 = 1$$B$H2>Dj$9$k!%<0(B(2)$B$K$*$$$F(B$x$$B$N9b<!$N9`$rE83+$9$k!%$9$k$H<!$rF@$k!%(B
$$ \begin{array}{l}
 \dot{x} = - \frac{1}{2} x^3 y, \\
 \dot{y} = - x^4 + x^6 \rho^2 + m_2 g_1(x,r,\phi) + O(m_3,m_2^2), \\
 \dot{\rho} = m_2 g_2(x,r,\phi) + O(m_3,m_2^2), \\
 \dot{\theta} = x^4 \rho, \\
 \dot{z} = w - x^4 \rho z i, \\
 \dot{w} = - |z|^{-3} z - x^4 \rho wi + O(m_3). 
   \end{array}             \eqno(7)
$$
$B$3$3$G4X?t(B$g_1(x,r,\phi)$$B$*$h$S(B$g_2(x,r,\phi)$$B$O0J2<$N$h$&$KDj5A$5$l$k!%(B
$$ \begin{array}{ll}
 g_1(x,r,\phi) = x^4 + 2x^6 r \cos \phi + 
\frac{\displaystyle -x^4 + x^6 r \cos \phi} 
     {\displaystyle (x^4 - 2x^2 r \cos \phi + 1)^{3/2}}, \\
 g_2(x,r,\phi) = - x^6 r \sin \phi + 
\frac{\displaystyle x^6 r \sin \phi} 
     {\displaystyle (x^4 - 2x^2 r \cos \phi + 1)^{3/2}}. \\
   \end{array} 
$$
$BJ}Dx<0$O(B$\theta$$B$K0MB8$7$J$$$3$H$KCm0U$9$k!%$@$+$i(B$\theta$$B$K4X$9$k<0$OMn$H$;$k$N$G$"$k!%(B

$B$^$:Bh;0BN$N<ANL$,L58B>.$N>l9g$r9M$($h$&!%(B$m_3=0$$B$HCV$1$P$$$o$f$kBJ1_@)8B;0BNLdBj$,F@$i$l$k!%$3$N>l9g(B$m_1$$B$H(B$m_2$$B$N50F;$O$-$A$s$HF@$i$l$k!%<!$NDL$j$G$"$k!%(B
$$ \begin{array}{l}
 r = \frac{\displaystyle a(1-e^2)}
          {\displaystyle 1+e \cos(\phi+\theta)}, \\
\phi + \theta = \phi_0 + \theta_0 + a^{-3/2} (t + 2e \sin t) + O(e^2). 
   \end{array} 
$$
$B$3$3$G(B
$$ \begin{array}{lcl}
 a = \left( \frac{\displaystyle -2h}{\displaystyle m_2(1-m_2)} \right)^{-1} & $B$*$h$S(B &  e = \left( 1 + 2 \frac{\displaystyle hC^2}{\displaystyle m_2^3(1-m_2)^3} \right)^{1/2}.   
\end{array} 
$$
$B$3$3$G(B$h$$B$H(B$C$$B$O$=$l$>$l7O$N%(%M%k%.!<$H3Q1?F0NL$G$"$k!%0lHL@-$r<:$&$3$H$J$/D9$5$NC10L$r(B$a=1$$B$H$J$k$h$&$K$D$M$KA*$Y$k!%$3$l$O(B$h=-\frac{1}{2}m_2(1-m_2)$$B$K$7$?$N$HF1$8$3$H$G$"$k!%(B

$e=0$$B$N$H$-!"$D$^$j(B$2hC^2 + m_2^3(1-m_2)^3=0$$B$N$H$-!"F@$i$l$k7O$O$$$o$f$k1_@)8B;0BNLdBj$G$"$k!%$3$NLdBj$N>l9g!"7O$O(B\underline{Jacobi$B@QJ,(B}$B$H8F$P$l$k$b$&$R$H$D$N@QJ,$r;}$D!%(B
$$
 \frac{1}{2} y^2 + \frac{1}{2} x^4 \rho^2 - U - \rho = J.   \eqno(8)
$$
$B$3$3$G(B$J$$B$O(B\underline{Jacobi$BDj?t(B}$B$G$"$j!"(B$U$$B$O(B$m_1$$B$H(B$m_2$$B$N=ENO>l$N%]%F%s%7%c%k4X?t$G$"$k!%(B
$$
  U = x^4 + m_2 x^2 \left( 
-1 - x^2 r \cos \phi + 
\frac{\displaystyle 1}{\displaystyle (1 - 2x^2 r \cos \phi + x^4)^{3/2}} \right) + O(m_2^2).
$$

$B>e$G$N5DO@$rF05!$H$7$F!"$3$s$I$O>.$5$$$1$l$I$b(B$e \neq 0$$B$*$h$S(B$m_3 \neq 0$$B$J$k40A4$J;0BNLdBj$r9M$($h$&!%$o$l$o$l$N5DO@$K9g$&$h$&$J7A$K1?F0J}Dx<0$r3,?t9_2<$9$k$3$H$KEX$a$k!%$^$:!"<0(B(8)$B$r?7$7$$JQ?t(B$J$$B$NDj5A$H$7$F;H$&!%(B$J$$B$O40A4$J;0BNLdBj$G$O$b$O$d1?F0$NDj?t$G$O$J$$!%(B
$$
  w = R e^{i \Phi},
$$
$B$H$*$1$P!"%(%M%k%.!<@QJ,$H3Q1?F0NL@QJ,$O<!$N7A$r$H$k!%(B
$$ \begin{array}{c}
\frac{\displaystyle 1}{\displaystyle 2}R^2 - 
\frac{\displaystyle 1}{\displaystyle r} = m_2^{-1}(1-m_2)^{-1}h + O(m_3) = - \frac{\displaystyle 1}{\displaystyle 2} + O(m_3), \\
Rr \sin(\Phi - \phi) = m_2^{-1}(1-m_2)^{-1}C + O(m_3) = 
\sqrt{1-e^2} + O(m_3) . 
   \end{array} 
$$
$r$$B$H(B$R$$B$KBP$9$k>e$N(B2$B$D$N<0$r(B$\phi$$B$H(B$\Phi$$B$K$h$C$F2r$/$3$H$,$G$-$F!"(B
$$ \begin{array}{l}
 r = r(\phi,\Phi,e) = 1 + O(m_3,e), \\
 R = R(\phi,\Phi,e) = 1 + O(m_3,e). 
   \end{array} 
$$
$B$3$s$I$OFHN);~4VJQ?t$r(B$t$$B$+$i(B$\phi$$B$KCV$-49$($k!%4JC1$J7W;;$K$h$l$P(B
$$
  \frac{\displaystyle d\phi}{\displaystyle dt} = 
1 - x^4 \rho + O(m_3,e),
$$
$B$G$"$j!"$^$?<0(B(7)$B$r<!$N7A$K=q$-49$($k$3$H$,$G$-$k!%(B
$$ \begin{array}{l}
\displaystyle  \frac{dx}{d\phi} = \displaystyle 
- \frac{ \frac{1}{2} x^3 y}{1 - x^4 \rho} + O(m_3,e), \\ 
\displaystyle \frac{dy}{d\phi} = \displaystyle 
 \frac{-x^4 + x^6 \rho^2 + m_2g_1(x,r,\phi)}{1 - x^4 \rho} 
+ O(m_3,m_2^2,e), \\ 
\displaystyle \frac{dJ}{d\phi} = 
m_2 e F(x,y,J,\Phi,\phi) + O(m_3,m_2^2,e^2), \\  
\displaystyle \frac{d\Phi}{d\phi} = 1 + O(m_3,m_2,e).
   \end{array}                  \eqno(9)
$$
$B$3$3$G(B$F$$B$O(B$x,y,J,\Phi$$B$*$h$S(B$\phi$$B$N4X?t$G$"$k!%(B$F$$B$NL@<(E*$J7A$O8e$GM?$($k!%(B

$B<0(B(9)$B$GDj5A$5$l$kN.$l$O#4<!856u4V$N$J$+$G;~4V$K0MB8$9$k!%$o$l$o$l$O(B$m_2,e$$B$*$h$S(B$m_3$$B$,>.$5$$7O$N2r$K6=L#$,$"$k!%$3$NL\E*$N$?$a$K!"$5$i$K:BI8JQ49$r$9$k$N$,ET9g$h$$!%<!$N$h$&$K$*$/!%(B
$$
  u e^{(\phi - \psi)i} = e^{\phi i} + 
R^2 r \sin(\Phi-\phi) i e^{\Phi i}.    \eqno(10)
$$
$u$$B4X$9$k>e$N<0$O2r$/$3$H$,$G$-$F!"(B$u=e + O(m_3)$$B$G$"$k$3$H$,$o$+$k!%(B$u$$B$,%<%m$G$J$1$l$P(B($B$3$l$O(B$0 \leq m_3 \ll e$$B$J$i$D$M$K@5$7$$(B)$B!"(B$\psi$$B$K4X$9$k<0$r2r$/$3$H$,$G$-$k!%(B$\psi$$B$rFHN)JQ?t$H$7$FMQ$$!"(B$\Phi$$B$HCV$-49$($h$&!%D9$C$?$i$7$$>\:Y$r>J$$$F!"1?F0J}Dx<0$r(B$x,y,J$$B$*$h$S(B$\psi$$B$H?7$7$$;~4VJQ?t(B$\phi$$B$G=q$1$P!"(B
$$ \begin{array}{l}
 \frac{\displaystyle dx}{\displaystyle d\phi} = 
- \frac{\displaystyle \frac{1}{2} x^3 y}{\displaystyle 1 - x^4 \rho} + 
O(m_3,e), \\ 
 \frac{\displaystyle dy}{\displaystyle d\phi} = 
 \frac{\displaystyle -x^4 + x^6 \rho^2 + m_2g_1(x,r,\phi)}
     {\displaystyle 1 - x^4 \rho} + O(m_3,m_2^2,e), \\ 
 \frac{\displaystyle dJ}{\displaystyle d\phi} = 
\frac{\displaystyle -2m_2 e x^4 \sin \phi \cos \psi}
     {\displaystyle 1 - x^4 \rho}  \left( -1 + 
\frac{\displaystyle 3}{\displaystyle (1-2x^2\cos \phi + x^4)^{5/2}} 
\right) + O(m_3,m_2^2,e^2), \\
 \frac{\displaystyle d\psi}{\displaystyle d\phi} = 
\frac{\displaystyle 1}{\displaystyle 1 - x^4 \rho} + O(e,m_3).
   \end{array}                  \eqno(11)
$$

$B>e$N<0$O(B$\psi$$B$,(B(10)$B<0$G2r$1$k$H$-$@$1@5$7$$$3$H$rCm0U$7$F$*$/!%$3$l$r@.$jN)$?$;$k$?$a$K!"(B$0 \leq m_3 \ll e$$B$rMW@A$9$k!%$7$+$7!"(B$m_3=e=0$$B$N$H$-1?F0J}Dx<0$O(B$\psi$$B$K0MB8$7$J$$!%$@$+$i$=$NCM$OG$0U$K;XDj$G$-!"$7$+$b<0(B(11)$B$O$J$*@5$7$$!%(B

\vspace{0.5cm}
\noindent
{\bf 5. $B@)8B;0BNLdBj(B}

$B$3$N@a$G$O(B$m_3=e=0$$B$N>l9g$r5DO@$9$k!%$3$N>r7o$GF@$i$l$k7O$O1_@)8B;0BNLdBj$^$?$OC1$K@)8B;0BNLdBj$G$"$k!%1?F0J}Dx<0$O<!$N$h$&$K4JC1$K$J$k!%(B
$$ \begin{array}{l}
\displaystyle \frac{dx}{d\phi} = \displaystyle 
- \frac{\frac{1}{2} x^3 y}{1 - x^4 \rho}, \\  
\displaystyle \frac{dy}{d\phi} = \displaystyle 
\frac{-x^4 + x^6 \rho^2 + m_2g_1(x,r,\phi)}{1 - x^4 \rho} + O(m_2^2), \\
\displaystyle \frac{dJ}{d\phi} = 0, \\
\displaystyle \frac{d\psi}{d\phi} = \displaystyle 
\frac{1}{1 - x^4 \rho}.
   \end{array}                  \eqno(12)
$$
$B>e$N<0$G$D$M$K(B$r=1$$B$G$"$j!"(B
$$ \begin{array}{l}
 \rho = \displaystyle \rho_0 - \frac{m_2x^2}{1 - x^4 \rho_0} 
\left( -1 -x^2 \cos \phi + 
\frac{1}{(1 - 2x^2 \cos \phi + x^4)^{3/2}} \right) + O(m_2^2), \\ 
 \rho_0 = \displaystyle 
\frac{1 \pm \sqrt{1 - x^4(y^2 - 2x^2 - 2J)}}{x^4}, 
   \end{array}                               \eqno(13)
$$
$B$G$"$k!%$?$@$7Id9f(B$\pm$$B$O(B$m_3$$B$NAjBPE*3QB.EY$K0MB8$9$k!%(B

$B$5$F(B$J$$B$O1?F0$NDj?t$G$"$k!%$3$l$OA0$K5DO@$7$?@)8B;0BNLdBj$N%d%3%S@QJ,$G$"$k!%>e$N(B$x$$B$*$h$S(B$y$$B$KBP$9$kJ}Dx<0$O(B$\psi$$B$K0MB8$;$:$7$?$,$C$FFHN)$K2r$1$k!%(B

$m_2=0$$B$J$i>e$NLdBj$O$5$i$KFsBNLdBj$K5"Ce$9$k!%$9$k$H(B$\rho=-J$$B$O1?F0$NDj?t$G!"1?F0J}Dx<0$O$5$i$K4JC1$J<!$N7A$K$J$k!%(B
$$ \begin{array}{l}
 \frac{\displaystyle dx}{\displaystyle d\phi} = 
- \frac{\displaystyle \frac{1}{2} x^3 y}{\displaystyle 1 + x^4 J}, \\  
 \frac{\displaystyle dy}{\displaystyle d\phi} = 
 \frac{\displaystyle -x^4 + x^6 \rho^2}{\displaystyle 1 + x^4 J}, \\ 
 \frac{\displaystyle dJ}{\displaystyle d\phi} = 0, \\
 \frac{\displaystyle d\psi}{\displaystyle d\phi} = 
\frac{\displaystyle 1}{\displaystyle 1 + x^4 J}.
   \end{array}                  \eqno(14)
$$
$B>e$NJ}Dx<07O$O40A42D@QJ,$G$"$k!%<!$N$h$&$K$*$3$&!%(B
$$
 H(x,y,J) = \frac{1}{2}y^2 + \frac{1}{2}x^4J^2 - x^2.
$$
$B4JC1$KJ,$+$k$h$&$K!"(B$H(x,y,J)$$B$O1?F0$NDj?t$G$"$k!%$3$l$OBh;0BN$N%(%M%k%.!<$r$=$N<ANL(B($BL58B>.(B)$B$G<\EYJQ49$7$?$b$N$G$"$k!%(BFigure 1$B$O!"%<%m$G$J$$(B$J$$B$r8GDj$7$F4X?t(B$H(x,y,J)$$B$N(B$x-y$$BJ?LL$N%l%Y%k6J@~$r<($7$F$$$k!%(B

\vspace{3.0cm}
\hspace*{6cm} Figure 1

\vspace{3.5cm}
$B%Y%/%H%k>l(B(14)$B$GM?$($i$l$kN.$l$r(B$x-y$$BLL$K<M1F$9$l$P!"86E@(B$(0,0)$$B$,N.$l$NFC0[E@$G$"$k$3$H$,$o$+$k!%J}Dx<0$N0x;R(B$x^3$$B$N$*$+$2$GFC0[@-$OAP6JE*$G$J$$!%$7$+$70x;R(B$x^{-3}$$B$G;~4V$N<\EYJQ49$r$9$l$P(B$(0,0)$$B$,AP6J%5%I%kE@$G$"$k$3$H$,$o$+$k!%%5%I%kE@$r$=$l<+?H$K7k$V%[%b%/%j%K%C%/%k!<%W$,$"$k!%J*M}E*$K$O$3$N%[%b%/%j%K%C%/%k!<%W$OFsBNLdBj$NJ|J*50F;$KBP1~$9$k!%0J8e$N2r@O$O<g$H$7$F$3$N%[%b%/%j%K%C%/%k!<%W$K4p$E$$$F$$$k!%$7$+$7$3$N%[%b%/%j%K%C%/%k!<%W$r;~4VJQ?t(B$\phi$$B$rMQ$$$FL@<(E*$K=q$-2<$9$N$OFq$7$$!%(B$x = \xi(\phi)$$B$*$h$S(B$y = \eta(\phi)$$B$O%[%b%/%j%K%C%/%k!<%WFb$N2r$G$"$C$F(B$\eta(0)=0$$B$G$"$k$H$9$k!%$3$N$H$-(B$\xi(\phi(t))$$B$*$h$S(B$\eta(\phi(t))$$B$O<!$N$h$&$JL@<(E*$J7A$r$H$k!%(B

$$ \begin{array}{l}
 \xi(t,\rho) = \displaystyle 
\frac{\sqrt{2}}
{\sqrt{\left( 3t + \sqrt{9t^2 + \rho^6} \right)^{2/3} + 
\left( 3t - \sqrt{9t^2 + \rho^6} \right)^{2/3} - \rho^2}}, \\ 

 \eta(t, \rho) = \left\{ \begin{array}{lcl}
   \pm \sqrt{2 \xi^2(t) - \xi^4(t)\rho^2} & {\rm for} & x \geq 0, \\
   \mp \sqrt{2 \xi^2(t) - \xi^4(t)\rho^2} & {\rm for} & x \leq 0. 
                         \end{array} \right. 
   \end{array}                               \eqno(15)
$$
$B$3$3$G(B$\pm$$B$O(B$\rho$$B$NId9f$K0MB8$9$k!%8e$N$?$a$K!"%k!<%W$O(B$x$$B<4$r(B$\sqrt{2}|J|^{-1}$$B$G2#@Z$k$3$H!"$D$^$j(B$\xi(0) = \sqrt{2}|J|^{-1}$$B$G$"$k$3$H$r;XE&$7$F$*$/!%$H$/$K(B$J= \pm \sqrt{2}$$B$N$H$-!"%k!<%W$O(B$x$$B<4$r(B$x=1$$B$G2#@Z$k!%(B

$B>e$NFC0[E@!"86E@(B$O$$B!"$O(B$x-y$$BLL$G$O<B:]$K$O%Y%/%H%k>l(B(14)$B$N<~4|50F;$G$"$k$3$H$KCm0U$9$k!%(B

$B$5$F!"(B(12)$B<0$GM?$($i$l$kN.$l$G!"(B$m_2$$B$,>.$5$$$1$l$I$b%<%m$G$J$$>l9g$KLa$m$&!%$O$8$a$K(B$J$$B$r8GDj$7(B$\psi$$B$N<0$rMn$H$9!%(B

$BG$0U$N(B$\phi_0 \in [0,2\pi)$$B$KBP$7$F!"(B$\Sigma^{\phi_0}$$B$O(B$\phi=\phi_0$$B$GDj5A$5$l$kCGLL$H$9$k!%(B$\Pi$$B$O(B$\Sigma^{\phi_0}$$B>e$KDj5A$5$l$?Bh0l2s5"<LA|(B($B%]%"%s%+%l<LA|(B)$B$G$"$k$H$9$k!%86E@(B$O$$B$,(B$\Pi$$B$NITF0E@$G$"$k$3$H$O4JC1$K$o$+$k!%$3$NITF0E@$O=LB`$7$F$$$k!%$7$+$7!"(BMcGehee$B$NDjM}(B[11]$B$^$?$O(BRobinson$B$NDjM}(B2.1[16]$B$K$h$j!"$3$N>l9g$bITF0E@$X$N(B1$B<!850BDjB?MMBN(B$W^s(O)$$B$*$h$S(B1$B<!85IT0BDjB?MMBN(B$W^u(O)$$B$,$"$k!%$5$i$K!"$3$l$i$NB?MMBN$O(B$x>0$$B$N$H$-<B2r@OE*$G$"$k!%(BXia[21]$B$K$h$l$P$$$/$D$+$NITO"B3$J%d%3%SDj?t(B$J$$B$NCM$r=|$$$F!"(B$W^s(O)$$B$H(B$W^u(O)$$B$O(B$m_2$$B$,>.$5$$$H$-2#CGE*$K8r$o$k!%$3$N2#CGE*%[%b%/%j%K%C%/50F;$N$=$P$K$*$$$F$3$=!"(B$e$$B$H(B$m_3$$B$NCM$,%<%m$G$O$J$$$1$l$I$b>.$5$$$H$-!"$9$J$o$A!"40A4$JJ?LL;0BNLdBj$K$*$$$F!"$o$l$o$l$O$$$o$f$k%"!<%N%k%I3H;6$NHs>o$KJ#;($JNO3X$H8=>]$,8=$o$l$k$3$H$r<($9!%(B

$B@)8B;0BNLdBj$NBP>N@-$h$j!"0[$J$k%[%b%/%j%K%C%/E@$,(B2$B$D$"$k!%:G=i$N$b$N$OCGLL(B$\Sigma^{\phi_0=0}$$B>e(B$x$$B<4>e$K$"$j!"(B2$BHVL\$N$b$N$O(B$\Sigma^{\phi_0=\pi}$$B>e(B$x$$B<4>e$K$"$k!%D>4QE*$K$O!"L58B>.$N<AE@(B$m_3$$B$r(B$m_1$$B$H(B$m_2$$B$r7k$VD>@~>e$KCV$$$F!"(B$m_3$$B$NB.EY$rD4@a$7$F$=$N50F;$,(B$\omega$$BJ|J*E*$K$J$k$h$&$K$G$-$k!%BP>N@-$K$h$j!"(B$m_3$$B$N50F;$O(B$\alpha$$BJ|J*E*$G$b$"$k$+$i!"L58B1s(B($B$o$l$o$l$N:BI8$G$O86E@(B)$B$K$*$1$k<~4|50F;$X$N%[%b%/%j%K%C%/50F;$G$"$k!%D>@~>e$K(B3$BN3;R$rG[CV$9$k(B2$B$D$N0[$J$k$d$jJ}$+$i(B2$B$D$N0[$J$k%[%b%/%j%K%C%/E@$,F@$i$l$k(B(Fig.2$B;2>H(B)$B!%(B$p$$B$*$h$S(B$\overline{p}$$B$rBh0l$*$h$SBhFs$N%[%b%/%j%K%C%/E@$H$7!"(B$\gamma$$B$*$h$S(B$\overline{\gamma}$$B$r$=$l$i$N50F;$H$9$k!%8e$N$?$a$K!"(B$p$$B$N50F;(B$\gamma$$B$,FsBNLdBj$NJ|J*50F;(B$(\xi(\phi), \eta(\phi)), -\infty< \phi < \infty$$B$K$h$C$F$9$Y$F$N;~4V$K$o$?$C$F0lMM$K6a;w$G$-$k$3$H$r;XE&$7$F$*$/!%(B
$BF1MM$K!"(B$\overline{p}$$B$N50F;(B$\overline{\gamma}$$B$b(B$(\xi(\phi+\pi),\eta(\phi+\pi))$$B$K$h$C$F(B$-\infty < \phi < \infty$$B$N$9$Y$F$K$o$?$C$F0lMM$K6a;w$G$-$k!%(BXia[21]$B$N7k2L$K$h$j!"$$$/$D$+$NITO"B3$J%d%3%SDj?t(B$J$$B$NCM$r=|$$$F!"$^$?>.$5$J(B$m_2$$B$KBP$7$F!"%[%b%/%j%K%C%/50F;(B$\gamma$$B$O2#CGE*$G$"$k!%0BDj$*$h$SIT0BDjB?MMBN$N2r@O@-$K$h$j!"(B$\overline{\gamma}$$B$b$9$Y$F$N>.$5$J(B$m_2$$B$NCM$KBP$7$F$^$?(B$J$$B$N$"$kITO"B3=89g$r=|$$$F2#CGE*$G$"$k!%(B

\vspace{1.5cm}
\hspace*{6cm} Figure 2

\vspace{1.5cm}
$R$$B$O>.$5$JD9J}7A$G!"D:E@$O%[%b%/%j%K%C%/E@(B$p$$B>e$K$"$j!"(B2$B$D$NJU$O(B$W^s(O)$$B$H(B$W^u(O)$$B$N0lIt$G$"$k$H$9$k(B(Fig.3$B;2>H(B)$B!%(B$\Pi$$B$ODj5A$5$l$k8B$jBh0l2s5"<LA|$G$"$k$H$9$k!%(B

$BE@(B$q \in R$$B$KBP$7$F!"(B$k = k(q)$$B$O(B$\Pi^k(q) \in R$$B$J$k:G>.$N@5@0?t$H$9$k(B($B$?$@$7B8:_$9$k$H$7$F(B)$B!%$3$N$h$&$J(B$k>0$$B$,B8:_$9$kE@(B$q \in R$$B$9$Y$F$N=89g$r(B$D$$B$H$9$k!%<!$N$h$&$K$*$/!%(B
$$ \begin{array}{lcl}
  \tilde{\Pi}(q) = \Pi^k(q) & {\rm for \ all} & q \in D.
   \end{array} 
$$
$B$3$N<LA|(B$\tilde{\Pi}$$B$O!"(B$R$$B$KBP$9$k(B$\Pi$$B$N(B\underline{$B2#CG(B}$B<LA|$H8F$P$l$k!%(B$D$$B$O6u$G$J$$=89g$G$"$j!"$5$i$KL58B$KB?$/$N5-9f$+$i$J$k?d0\(B(shift)$BF1Aj<LA|$r(B$D$$B$KKd$a9~$a$k$3$H$,<($;$k!%$b$C$H@53N$K$O!"<!$N8EE5E*%[%b%/%j%K%C%/E@DjM}$,@.$jN)$D(B(Moser[13]$B;2>H(B)$B!%(B

\vspace{3.5cm}
\hspace*{6.0cm} Figure 3

\vspace{3.5cm}
\noindent
{\bf $BDjM}(B 5.1.} $B2#CG<LA|(B$\tilde{\Pi}$$B$NITJQItJ,=89g(B$I \subset D$$B$,B8:_$7$F=89g(B$S = {\bf N}^Z$($BL58B8D$N5-9f>e$NN>L58BNs$N6u4V(B)$B$KF1Aj$G$"$j!"$^$?(B$I$$B>e$N2#CG<LA|(B$\tilde{\Pi}$$B$O(B$S$$B>e$N?d0\<LA|$K0LAj6&Lr$G$"$k!%498@$9$l$P!"(B$\tau$$B$,F1Aj<LA|(B$\tau:S \rightarrow I$$B$G$"$C$F!"(B$\sigma$$B$,(B$S$$B$N?d0\<LA|$G$"$k$H$9$k!%$3$N$H$-<!$,@.$jN)$D!%(B
$$ 
  \tilde{\Pi} \tau = \tau \sigma.
$$

\vspace{0.3cm}
$\phi_0=0$$B$J$k2#CGLL(B$\Sigma^{\phi_0}$$B$r8GDj$7$h$&!%$3$N2#CGLL>e$G!"BP>N@-$K$h$j!"2#CGE*%[%b%/%j%K%C%/E@(B$p$$B$O(B$x$$B<4>e$K$"$k!%;v<B!"0BDj$^$?$OIT0BDjB?MMBN$KB0$9$kE@$G(B$x$$B<4>e$K$"$kG$0U$NE@$O%[%b%/%j%K%C%/50F;$r@8$8$k!%8e$N$?$a$K!"G$0U$N(B$\varepsilon>0$$B$*$h$S@5@0?t(B$k$$B$KBP$7$F!"86E@$N6aK5$KL58B$KB?$/$N%[%b%/%j%K%C%/E@$,$"$C$F!"$=$N50F;$O(B$p$$B$N50F;$N(B$\varepsilon$$B6aK5$K$"$j!"(B$p$$B$N6a$/$r(B$2k$$B2sDL2a$9$k$3$H$r;XE&$7$F$*$/!%(B

$B$3$NO@J8A4BN$rDL$7$F!"(B$t$$B$NBe$o$j$K(B$\phi$$B$rFHN);~4VJQ?t$H$7$F;H$&$3$H$r6/D4$7$F$*$/!%(B

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$n$$B$rBg$-$/$H$C$F<~4|2r(B$p_n$$B$r8GDj$9$k!%4JC1$K$o$+$k$h$&$K!"Bh0l2s5"<LA|(B$\Pi$$B$G$N(B$p_n$$B$N<~4|$O(B$n$$B$G$"$j!"2#CG<LA|(B$\tilde{\Pi}$$B$G$N<~4|$O(B1$B$G$"$k(B($\Pi^n = \tilde{\Pi}$$B$G$"$C$?$3$H$r;W$$$@$=$&(B)$B!%(B

$B$3$s$I$O<0(B(12)$B$N40A4$JAj6u4V$r9M$(!"J}Dx<0$N3QJQ?t(B$\psi$$B$r9MN8$KF~$l$h$&!%$3$N>u67@_Dj$G$O!">e$N<~4|50F;$NBgB??t$O$b$O$d<~4|E*$G$O$J$/!"$`$7$m=`<~4|2r$KBP1~$9$k!%(B$\Omega_n$$B$O<!<0$GM?$($i$l$k=89g$H$9$k!%(B
$$
  \Omega_n = \{ (x,y,J,\psi,\phi)|(x,y) = p_n(J); \phi=0; \psi \in S^1; J \in T \subset {\bf R} \}.
$$
$B$3$3$G(B$T$$B$O<B?tD>@~$N6h4V(B$T=(\sqrt{2}+\delta_1,\sqrt{2}+\delta_2)$$B$G!"(B$\delta_2>\delta_1>0$$B$O>.$5$$!%(B$\delta_1$$B$H(B$\delta_2$$B$NCM$O8e$G7h$a$k!%$3$N$H$-(B$\Omega_n$$B$O(B$\tilde{\Pi}$$B$NITJQ=89g$G$"$j!"@55,AP6JE*$G$"$k!%(B$\tilde{\Pi}_n$$B$O(B$\tilde{\Pi}$$B$r=89g(B$\Omega_n$$B$K@)8B$7$?<LA|$H$9$k!%(B$\delta_2>\delta_1>0$$B$,>.$5$$$H$-$3$N<LA|(B$\tilde{\Pi}_n$$B$,$M$8$l<LA|$G$"$k$3$H$r<($=$&!%1_4D>e$N$M$8$l<LA|$O3FF1?41_$r0lMM$K2sE>$9$kLL@QJ]B8<LA|$G$"$C$F!"2sE>NL$OF1?41_$NH>7B$H$H$b$KC1D4$KJQ$o$k$h$&$J<LA|$G$"$k$3$H$r;W$$$@$=$&!%(B

$J \in T$$B$H(B$\psi \in S^1$$B$r=89g(B$\Omega_n$$B$N6I=j:BI8$H$7$F;H$($k!%(B
