N = 50;
dx = pi/N;
X = -pi:dx:pi;

figure(1)
clf
plot(X,ones(size(X)));
hold on
plot(X,-ones(size(X)));
plot(X,zeros(size(X)));
mu = 1;
geuler = 1+2*mu*cos(X)-2*mu;
plot(X,geuler,':','LineWidth',2);
mu = 3/4;
geuler = 1+2*mu*cos(X)-2*mu;
plot(X,geuler,'-.','LineWidth',2);
mu = 1/2;
geuler = 1+2*mu*cos(X)-2*mu;
plot(X,geuler,'--','LineWidth',2);
mu = 1/4;
geuler = 1+2*mu*cos(X)-2*mu;
plot(X,geuler,'LineWidth',2);
axis([-pi,pi,-3,1.2])
xlabel('h \xi','FontSize',16)
print -dps g_euler.ps

figure(2)
plot(X,ones(size(X)));
hold on
plot(X,-ones(size(X)));
plot(X,zeros(size(X)));
mu = 1;
gimplicit = -1./(-1+2*mu*cos(X)-2*mu);
plot(X,gimplicit,':','LineWidth',2)
mu = 3/4;
gimplicit = -1./(-1+2*mu*cos(X)-2*mu);
plot(X,gimplicit,'-.','LineWidth',2)
mu = 1/2;
gimplicit = -1./(-1+2*mu*cos(X)-2*mu);
plot(X,gimplicit,'--','LineWidth',2)
mu = 1/4;
gimplicit = -1./(-1+2*mu*cos(X)-2*mu);
plot(X,gimplicit,'-','LineWidth',2)
axis([-pi,pi,-1.2,1.2])
xlabel('h \xi','FontSize',16)
print -dps g_implicit.ps

figure(3)
plot(X,ones(size(X)));
hold on
plot(X,-ones(size(X)));
plot(X,zeros(size(X)));
mu = 1;
gcrank = -(1+mu*cos(X)-mu)./(-1+mu*cos(X)-mu);
plot(X,gcrank,':','LineWidth',2);
mu = 3/4;
gcrank = -(1+mu*cos(X)-mu)./(-1+mu*cos(X)-mu);
plot(X,gcrank,'-.','LineWidth',2);
mu = 1/2;
gcrank = -(1+mu*cos(X)-mu)./(-1+mu*cos(X)-mu);
plot(X,gcrank,'--','LineWidth',2);
mu = 1/4;
gcrank = -(1+mu*cos(X)-mu)./(-1+mu*cos(X)-mu);
plot(X,gcrank,'-','LineWidth',2);
axis([-pi,pi,-1.2,1.2])
xlabel('h \xi','FontSize',16)
print -dps g_crank.ps