logistic_tent_conjugacy.html

CONJUGACY OF LOGISTIC AND TENT MAPS 1/26/2005
Logistic o H = H o Tent

> restart:
foo:=proc(x0)
T:=y->piecewise(y<0.5,2*y,2-2*y);
L:=x->4*x*(1-x);
h:=y->(1-cos(Pi*y))/2;
pL:=plot(L(x),x=0..1,color=red):
pT:=plot([T(y),y,y=0..1],color=blue):
ph:=plot([h(y),y,y=0..1],color=black):
ph2:=plot([y,h(y),y=0..1],color=black):
# x0:=0.3;
ps:=plot([[h(x0),L(h(x0))],[h(x0),x0],[T(x0),x0],[T(x0),h(T(x0))],[h(x0),L(h(x0))]],
color=green):
return plots[display](ps,pL,pT,ph,ph2);
end proc:

> foo(0.3);

> nsteps:=50;
plots[display]( seq(foo(i/nsteps),i=0..nsteps) ,scaling=constrained, insequence=true);