2.7 Resumen Variedad Estable
March 5, 2023 | Author: Anonymous | Category: N/A
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x2
s
X [
x2
K
@ : Ef ((x2 )
x˓ : @x
u
K
x˓ : f (( x)
φt
X [
X [
K s
K u
φt
nµİj φt (h) : x 2 , ∂h ∇ X ↝∙
t
nµİj φt (h) : x 2 , ∂h ∇ [.
t↝∝∙
x2
x2
x ↝ x ∝ x2
x˓ 0 : ∝ x0 x˓ = : ∝ x= + x== x˓ 8 : x 8 + x=0 .
∝0 2 2 (2) : 2 ∝0 2 (2)
@ : E Ef f
2
x8
K s
K u
2
0
x0 (t) : h 0 k∝t x= (t) : h = k∝t + h=0 k∝t ∝ k∝=t x8 (t) : h 8 kt +
8
∝ kt
k∝=t
h=0
x0 , x= x˓ 0 : ∝ x0
h : x (2)
nµİjt↝∝∙ φt (h) : 2
X [ : K u
]
h=0
8
h=0
8 :
h8 +
2
.
h0 : h = : 2
|h0 : h = : 2 .
]
|h8 : ∝
8
s
(K )
@ M
ΰ, [ ΰ ΰ
x0 , x=
[ ΰ
i ]
:
J
H a
ΰ [ ΰ
i ] | |x| > 0 }
M : {x ∇ M gΰ 4 [ ΰ ↝ M
i J {[ ΰ }
W @ M g 4 @ ↝ M
@ M
(=) [ ΰ ∣ [ ν : ∋ gΰ 4 [ ΰ ↝ M gν 4 [ ν ↝ M i gΰ ([ ΰ ∣ [ ν ) gν ([ ΰ ∣ [ ν ) ]
@ M
W
@ M
(0)
4 M ↝ @
g
∝0
8
h ∇
[ : h ∇
nµİjt↝∙ φt (h) : 2
X : :
0 g : g ΰ ◦ g∝ ν 4 g ν ( [ ΰ ∣ [ ν ) ↝ g ΰ ([ ΰ ∣ [ ν )
H a
ekt Eg (x) : 2
x ∇ gν ([ ΰ ∣ [ ν ) J
∝0
g : gΰ ◦ gν
∝0
f ∇ H
(K )
φt
K
i ]
(2) : 2 f (2)
(2) Ef (2)
a
K
s
2
i∝a X a t ≫ 2 , φt (X ) ⊍ X
x2 ∇ X
nµİj φt (x2 ) : 21
t↝∙
u
K
2
[ i∝a t ≥ 2 , φt ([ ) ⊍ [
x2 ∇ [
nµİj φt (x2 ) : 2.
t↝∝∙
f ∇ H 0 (K ) f (2) (2) : 2
(2) F (( x) : f (( x) ∝ @x F ∇ H 0 (K ) F (2) (2) : 2 EF (2) (2) : 2 @ : Ef (2) λ 9 2 ε 9 2 |x| ≥ ε |y | ≥ ε
iÜi
α0 ,....,α8 αa+0 ,....,αi ΰ 9 2
H
R 2 2 P
R a Ü a P (i ∝ a ) Ü (i ∝ a) d : 0,...,a,
y : H ∝0 x
˞ L (y ) : H ∝0 F (( H y ) ∇ H 0 K
˞ : H ∝0 (K ) L K
y˓ : M y + L (y )
]k (α d ) > ∝ ΰ > 2 .
M : H ∝0 @H :
|F (( x) ∝ F (( y )| ≥ λ |x ∝ y | .
x˓ : @x + F (( x)
u( d ) (t, `)
x˓ 0 : ∝ x0 ∝ x== x˓ = : x = + x=0 .
u(0) (t, `) , u(=) (t, `) u(8) (t, `)
u(2) (t, `) : 2 t
( d +0)
u
(t, `) : [ (t) `
+ 2
∙
( d )
(s, `
[ (( t ∝ s) L u
∝ ) es
t
( d )
V (t ∝ s) L u
(s, `) es.
u(8) (t, `)
χ=
X 4 4 x = : χ = (x0 ) .
∝0 2 : 2 0 2
@ : M
k∝t
[ (( t) :
2
+
2 k
`0
, ` :
t
,
.
2
∙
es ∝
2
2
L x
k∝(t∝s) u== (s)
∝
2
, F x
, V (t) :
t
k∝t `0
u (t, `) :
2
x== x=0
∝ (( ) : ( ) : 2 2
2
kt∝s u=0 (s)
t
es
u(2) (t, `) : 2 u(0) (t, `) : (=)
k∝t `0
2
∝
k∝t `50
k∝=t
`0 ↝ 2 .
x0 x=
x0 ↝ 2. (x) (y )
H : C
8
x0 ↝ 2 .
8
χ= (`0 ) : u = (2, `0 , 2)
X
[
t ↝ ∝t
+ 2 x;0
x==
s
es
+ 2 x;0
[ 4 x 0 : ∝
kt∝s k∝=t `=0
x=0
2
+ 2 `;0
8
es
x=0
4 x = : ∝ X 4
`0=
∙
.
= 8 `0
χ= (`0 ) : ∝
∝=t
k8
t
u(5) (t, `)∝u(8) (t, `) : 2 `;0
2 k∝5t
0 =<
k∝t `0
t
2
:
k∝t `0
2
es kt∝s k∝=s `=0 k∝(t∝s) k∝5t `50
t
k∝t `0
u(8) (t, `
: ∝ ∝ ∝ 0 ∝ ∝ 2 3 ∝ +
2
):
∙
k∝t `0
(t, `) :
u
K
K
X [ x˓ : @x
u
X
X [
[
2
X [
φt
2
\ s (2) :
φt (X )
φt ([ )
t≥2
\ u (2) :
t≫2
\ s (2) \ u (2)
s
u
\ (2) \ (2)
φt 1 nµİjt↝∝∙ φt (x) : 2
x ∇ \ s (2) nµİjt↝∙ φt (x) : 2
x ∇ \ u (2)
I X [
X : : { x ∇ I |φt (x) ↝ 2 }
t ↝ ∙ φt (x) ∇ I
t ≫ 2
[ : { x ∇ I |φt (x) ↝ 2 }
t ↝ ∝∙ φt (x) ∇ I
t ≥ 2
s
u
\ (2) \ (2)
s
\ (2)
u
\ (2)
t ≥ 2
|φt (x2 )| ≥ λk ∝νt
X [ ]kk (αj ) ]k (α d ) > ∝ΰ > 2 > ν > ] λ 9 2 ε 9 2
|φt (x2 )| ≥ λk ∝ΰt
t ≫ 2 x2 ∇ I ε (2) ∤ [
d : 0,...,a j : a + 0,...,i x2 ∇ I ε (2) ∣ X
h
i ]
r ≫ 0 dd
2
K
2
a
K
2
a j : i ∝ a ∝ \ h (2)
s
H
\ (2) d h s h \ (2) \ (2) \ (2)
u
f ∇ H r (K ) K (2) : 2 Ef (2) (2) f (2)
h
H
r
\ (2)
s
h
r
\ (2)
j
d
K
r
H
φt
2
u
K
x˓ 0 : x =0 x˓ = : ∝ x= .
h
K
K s
x0 .
x=
x0
h
H \ h (2)
∙
K
x0
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