clear all;



Niter = 10^4;   % number of initial x0
Nt=1;           % number of times to do the map


X0 = zeros(1,Nt);
X  = zeros(1,Nt);


for ia=1:Niter

m = 2/3;
s = 1/80;
x0 = m + s*randn(1); % choose a x0 from a gaussian distributions
                     % with mean m and variance s
x0 = mod(x0,1); % if x is outside [0,1] then put it inside by adding integers (see help mod)


X0(ia)=x0;% initial x
x=x0;

for it=1:Nt;
    
    if x<1/2
        xnew = 2*x;
    else
        xnew = 2*(1-x);
    end
    x=xnew;
end

X(ia) = x; % x after Nt steps

end;


[P0,x0] = hist(X0,20); 
dx0 = x0(2)-x0(1);
P0norm = P0/(Niter*dx0);

[P,x] = hist(X,20); 
dx=x(2)-x(1);
Pnorm = P/(Niter*dx);

%%
figure(3);clf;
plot(x0,P0norm,'g',x,Pnorm,'b','LineWidth',2);
hold on;
plot([0 1],[1 1],'--k')
hold off;

xlabel('x','FontSize',18);
ylabel('p(x)','FontSize',18);
pause(1)