% Schrodinger's equation on a lattice - ratio map
 clear u v x y;
%
 nn = 6;                 % fix integer for possible periodic solutions
 yy(1) = 1;              % initial condition
 ee = 2.*cos(pi./nn)+ .1;    % E = energy
 eps = .0;              % size of random perturbation
 steps = 6.*50;          % number of iterations
%
 for jj=1:steps
 yy(jj+1) = ee - 1./yy(jj) -eps.*randn(1);    % ratio map
 u(jj) = yy(jj);                              % save values for plotting
 v(jj) = yy(jj+1);                            
 end;
x = -5:.053:5;                                % curve describing the map
y = ee-1./x;                                  %
 hold 
 plot(x,y)                       % plot  nonlinear curve describing the map
 hold
plot(u,v,'-.*')                               %
%
% Calculate products to test growth
for k= 1:steps
produ(k) = prod(u(1:k));
slog(k) = mean(log(abs(u(1:k))));
end;
axis([-5 5 -10 10])