getf("sys_diff.sci");
//
// (a) Valeurs propres 0.1, 0.2
//
xset("window",0); xbasc();
ang=2*%pi/3;
rot=[cos(ang),-sin(ang);sin(ang),cos(ang)];
A=inv(rot)*[0.1,0;0,0.2]*rot;
deff("y=F1(t,x)","y=A*x");
tmax = 20; pas =0.01;
xy0=[0.1;0.1];
champxy(F1,xy0,tmax,pas);
//
// (b) Valeurs propres 0.1, -0.1
//
xset("window",1); xbasc();
ang=-2*%pi/3;
rot=[cos(ang),-sin(ang);sin(ang),cos(ang)];
A=inv(rot)*[0.1,0;0,-0.1]*rot;
deff("y=F2(t,x)","y=A*x");
tmax=10; pas=0.01;
xy0=[0.1;0.1];
champxy(F2,xy0,tmax,pas);
//
// (c) Valeurs propres -0.1, -0.2
//
xset("window",2); xbasc();
ang=-2*%pi/3;
rot=[cos(ang),-sin(ang);sin(ang),cos(ang)];
A=inv(rot)*[-0.1,0;0,-0.2]*rot;
deff("y=F3(t,x)","y=A*x");
tmax=100; pas=0.01;
xy0=[1.9;1.9];
champxy(F3,xy0,tmax,pas);
//
// (d) Valeurs propres 0.1+0.3 i, 0.1-0.3 i
//
xset("window",3); xbasc();
module=sqrt((0.1)^2+(0.3)^2);
ang=acos(0.1/module);
rot=[cos(ang),-sin(ang);sin(ang),cos(ang)];
A=module*rot;
deff("y=F4(t,x)","y=A*x");
tmax=50; pas=0.01;
xy0=[0.1;0.1];
champxy(F4,xy0,tmax,pas);
//
// (e) Valeurs propres -0.1+0.3 i, -0.1-0.3 i
//
xset("window",4); xbasc();
module=sqrt((0.1)^2+(0.3)^2);
ang=acos(-0.1/module);
rot=[cos(ang),-sin(ang);sin(ang),cos(ang)];
A=module*rot;
deff("y=F5(t,x)","y=A*x");
tmax=50; pas=0.01;
xy0=[1.7;1.7];
champxy(F5,xy0,tmax,pas);
//
// (f) Valeurs propres i, -i
//
xset("window",5); xbasc();
A=[0,1;-1,0];
deff("y=F6(t,x)","y=A*x");
tmax=10; pas=0.01;
xy0=[1;1];
champxy(F6,xy0,tmax,pas);




