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Classroom Notes: Pursuit Curves in the Complex Plane
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8/12/2019 Classroom Notes: Pursuit Curves in the Complex
Plane
1/9
D 2013
A: A / .
D: (C) , ,( ) ( )k n k ng z z z = + z S , ( )k ng z S
S . ,
lim 0k n
n
= , () 1,2,...,k n= .
1, 1,( ) ( )n nG z g z= , ( ), , 1,( ) ( )k n k n k nG z g G z=
,( ) ( )n n nG z G z= ( ) lim ( )n
nG z G z
= ,
. .
0,1. , ( ) ( )z f z z = , f=F .
.
= +
=
,
= ( ) ( )z f z z = . , C
f=F C: = .
F , = = + = . F
{ }
=, = , C,
= = .
,
18
.
, ,
.
.
{ }
= { }
=
. .
.
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8/12/2019 Classroom Notes: Pursuit Curves in the Complex
Plane
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{ } , = , ,
:
(1)
= ,
(1) =
C (1)
C , (1)
. : C ,
= + , f=F (C
) (C ),
(1) (1), = .
.
D () ,
, .
= , = +
=
. = = + .
= +
= + ,
= ,
= + .
-
8/12/2019 Classroom Notes: Pursuit Curves in the Complex
Plane
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= , :
(1) = ,
.
= ,
= .
= , = + . = .
+
= + ,
+ , + .
+
=
0,1. B
:
(2)
=
(2) = =
.
= . C , ,
.
. ,
, :
= + + , = ; = , = , = .
= + + .
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8/12/2019 Classroom Notes: Pursuit Curves in the Complex
Plane
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= + + = + + ,
= = + .
= + + =
.
. ,
, ,
. (2) (2)
(2)
= + +
= [ ]
= ,
B = + +
= + .
( )
= + + .
=4+4.
= + , = , = . f=F
= + = +
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8/12/2019 Classroom Notes: Pursuit Curves in the Complex
Plane
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E , ,
. ,
, :
= + + , = , = = ,
= + +
= = + = + ,
= + = +
( )
= + + +
. .
.
,
. ( )
.
, :
(3)
= + , =
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8/12/2019 Classroom Notes: Pursuit Curves in the Complex
Plane
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= + + , = , = , = , *=.5.
= + + +
.
.
,
.
(4) = , , < >
= + , = = . =
+ .
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8/12/2019 Classroom Notes: Pursuit Curves in the Complex
Plane
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(
) .
. ( ) ,
.
,
,
. :
,
.
A , = + + ,
:
(5) ( )
= + + , ( )
= + + + + ,
( )
= ( )
= + .
( )
+ .
, C
. F ,
=
= = = +F .
A (5) , = .
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8/12/2019 Classroom Notes: Pursuit Curves in the Complex
Plane
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= + + +F . =
= . = + = + .
=
=
:
. C :
, ,
.
.
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8/12/2019 Classroom Notes: Pursuit Curves in the Complex
Plane
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, .
= + = +
= =
,
. F =
=
= . ,
,
=
,
=
, =
= .
= = = + ,
( )( )
= + = .
= , .
