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(O, i, j)
P P P1 2
ρ(x,y)
P A = (0,2) C = (0,−2) D = (−4,−2)1
E = (−4,2)
P2
2 xP = (x, y)∈R / 06 x6 2 et |y|6 (2−x)e2
P
A PP
x yG G
x yG G
D
2 2 2 2 2D = (x,y)∈R /x +y > 1 et x +y 6 2y
D
A DD
2 2I = (x +y )dxdy
D
I =]0,+∞[ t∈ I A(t)
 
t t 0 A(t) = 0 t t
0 t t

A(t)
A(t)
A(t)
−1D(t) Q A(t) = Q D(t) Q

−1• Q
I
˙X(t) = A(t)X(t) (S)
   
x (t) x˙ (t)1 1  ˙  X = x (t) et X = x˙ (t)2 2
x (t) x˙ (t)3 3
φ(t) (S)
φ(t) (S)
−1φ(t) (S) t ∈ I ψ(t) = Q φ(t) ψ(t)
˙Y(t) = D(t)Y(t) (S )1
˙Y Y(t)
a b c
 
a 2
t ψ(t) = 2b e 
2
tc e
φ(t) t a b c
x˙(t)−t x(t)−t y(t) = 0
y˙(t)−t y(t)−t z(t) = 0
z˙(t)−t y(t)−t z(t) = 0
x(0) = 1 y(0) = 2 z(0) = 44
3.5
3
2.5
2
1.5
1
0.5
0
−0.5
−1
−1.5
−2
−2.5
−3
−3.5
−4
−4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
X
44
3.5
3
2.5
2
1.5
1
0.5
0
−0.5
−1
−1.5
−2
−2.5
−3
−3.5
−4
−4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
X
D