Fig9.mw

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

> #A degenerate parabolic CR singularity,

> #deformed to a hyperbolic singularity

> z1*conjugate(z1)+(1/2+t2)*(z1^2+conjugate(z1)^2)+z1*conjugate(z1)*(z1^2+conjugate(z1)^2)+I*t1*(z1-conjugate(z1));

z1*conjugate(z1)+(1/2+t2)*(z1^2+conjugate(z1)^2)+z1*conjugate(z1)*(z1^2+conjugate(z1)^2)+I*t1*(z1-conjugate(z1))

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

(x+I*y)*(x-I*y)+(1/2+t2)*((x+I*y)^2+(x-I*y)^2)+(x+I*y)*(x-I*y)*((x+I*y)^2+(x-I*y)^2)-2*t1*y

> expand(%);

2*x^2+2*t2*x^2-2*t2*y^2+2*x^4-2*y^4-2*t1*y

> h2:=eval(%,{t1=0,t2=1/4});

h2 := 5/2*x^2-1/2*y^2+2*x^4-2*y^4

> plot3d(h2,x=-0.6..0.6,y=-0.6..0.6,contours=20,axes=boxed,style=patchcontour,shading=zgrayscale,tickmarks=[0,0,0],transparency=0.7,labels=["","",""]);

[Plot]