Fig5.mw

> restart;with(plots):interface(showassumed=0):assume(x,real);assume(y,real);

> #The nondegenerate parabolic case,

> #A totally real nearby deformation

> z1*conjugate(z1)+(1/2)*(z1^2+conjugate(z1)^2)+I*z1*conjugate(z1)*(z1-conjugate(z1))+I*t*(z1-conjugate(z1));

z1*conjugate(z1)+1/2*z1^2+1/2*conjugate(z1)^2+I*z1*conjugate(z1)*(z1-conjugate(z1))+I*t*(z1-conjugate(z1))

> eval(%,z1=x+I*y);

(x+I*y)*(x-I*y)+1/2*(x+I*y)^2+1/2*(x-I*y)^2-2*(x+I*y)*(x-I*y)*y-2*t*y

> expand(%);

2*x^2-2*y*x^2-2*y^3-2*t*y

> h2:=eval(%,t=0.1);

h2 := 2*x^2-2*y*x^2-2*y^3-.2*y

> plot3d(h2,x=-0.25..0.25,y=-0.25..0.25,contours=32,axes=boxed,style=patchcontour,shading=zgrayscale,tickmarks=[0,0,0],transparency=0.7,labels=["","",""]);

[Plot]