clear
close all
r =  0.8284
x = [-3 :0.03: 3];
y = [-3 :0.03: 3];
lx = size(x,2)
ly = size(y,2)


for i = 1 :ly
	for j = 1 :lx
      V1(i,j) = double((x(j)*y(i)+y(i)^2-1<0));
      V1bis(i,j) = double((x(j)*y(i)-1<0));
      
      V2(i,j) = double((x(j)^2 + y(i)^2<r));      
      Vins(i,j) = double(x(j)*y(i) > 2);
	end
end


figure(1)
subplot(221)
pcolor(x,y,Vins);
shading flat
title('\Omega 1 :xy<2')
subplot(222)
pcolor(x,y,V1);
title('\Omega 2 : xy+y²-1<0')
shading flat
subplot(223)
pcolor(x,y,V2);
shading flat
title('\Omega 3 : x²+y²-r<0')
subplot(224)
pcolor(x,y,V1+V2);
shading flat
title('intersection de \Omega 2 et \Omega 3')
colormap('gray')

Vt = V1bis+2*V1+3*V2+4*Vins;
figure(2)
pcolor(x,y,Vt/10)
colormap(jet)
shading flat


hold on

for i =1 : 5
    [x10 ,x20]=ginput(1)

    sim('Simu_Lyap_1',[0 3])
    t = plot(x1,x2,'k',x10,x20,'*k');
end

hold off