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( )( )
0|Re
0
=
′′
+
′′
=
= tytxt
yUxUtzS
dt
d
.
constzS
≡
)(Im
∗
γ
,
()( )
0|Im
0
=
′′
+
′′
=
= tytxt
yVxVtzS
dt
d
=
′′
+
′′
=
′
′
+
′
′
0
0
tytx
tytx
yVxV
yUxU
( )
xyyx
VUVU
′
−=
′
′
=
′
,
=
′′
−
′′
=
′
′
+
′
′
.0
0
tytx
tytx
xUyU
yUxU
( )
0
2
22
≠
′
−=
′
+
′
−=∆
ttt
zyx
,
(
)
(
)
(
)
(
)
0
0000
=
′
=
′
=
′
=
′
zVzVzUzU
yxyx
.
∗
γ
0
z
,
0)(
0
=
′
zS
.
,
.
4. (.)
( )
zU
D
D
.
( )
zU
,
.
5.
0
z
–
)(zS
, .
0)(,0)(
00
≠
′
′
=
′
zSzS
.
U
0
z
)(Re)(Re
0
zSzS =
,
0
z
U
.
( )
)()(Re
0
zSzS −
, ,
)(Re)(Re
0
zSzS <
,
∗
γ
,
, .
)(Re)(Re
0
zSzS <
)(Im)(Im
0
zSzS =
∗
∈γz
.
Re S (z (t )) |t =0 = U ′x xt′ + U ′y yt′ = 0 .
d
dt
Im S ( z ) ≡ const γ∗,
Im S ( z (t )) |t = 0 = V x′xt′ + V y′ y t′ = 0
d
dt
U ′x xt′ + U ′y yt′ = 0
′ ′
Vx xt + V y′ yt′ = 0
(U ′ = V ′, U ′ = −V ′)
x y y x
U ′x xt′ + U ′y yt′ = 0
′ ′
U x yt − U ′y xt′ = 0 .
( )
∆ = − xt′2 + yt′2 = − zt′ ≠ 0 ,
2
U ′x ( z0 ) = U ′y ( z0 ) = Vx′( z0 ) = V y′ ( z0 ) = 0 .
γ∗
z0 , S ′( z 0 ) = 0 .
,
.
4. ( .)
U (z )
D D. U (z ) ,
.
5. z0 – S (z ) , .
S ′( z 0 ) = 0, S ′′( z 0 ) ≠ 0 . U z0
Re S ( z ) = Re S ( z0 ) ,
z0 U .
Re(S ( z ) − S ( z0 ) ) , ,
Re S ( z ) < Re S ( z0 ) , γ∗,
, . Re S ( z ) < Re S ( z0 ) Im S ( z ) = Im S ( z 0 ) z ∈γ ∗ .
