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%% s3 b = 0.3; epsilon = 0.005; a_eps = 0.001; l = 2; x = linspace(-l, l, floor(1/epsilon)); y = linspace(-l, l, floor(1/epsilon)); a = linspace(a_eps, 10, floor(1/a_eps)); p_3 = zeros(floor(1/a_eps), floor(1/epsilon), floor(1/epsilon)); for i=1:floor(1/a_eps) for j=1:floor(1/epsilon) for k=1:floor(1/epsilon) p_3(i, j, k) = check_3_period(a(i), b, x(j), y(k), 0.0001); end end end if isequaln(p_3, zeros(floor(1/a_eps), floor(1/epsilon), floor(1/epsilon))) disp(":(") else non_zero = mod(find(p_3), floor(1/a_eps)).*10./floor(1/a_eps); non_zero = sort(non_zero); zero = find(~p_3); disp(non_zero) end %% s4 b = 0.3; a = 6; l = 10; epsilon = 0.005; x = linspace(-l, l, floor(1/epsilon)); y = linspace(-l, l, floor(1/epsilon)); p_3 = zeros(floor(1/epsilon), floor(1/epsilon)); for j=1:floor(1/epsilon) for k=1:floor(1/epsilon) p_3(j, k) = check_3_period(a, b, x(j), y(k), 0.0001); end end if isequaln(p_3, zeros(floor(1/epsilon), floor(1/epsilon))) disp(":(") else non_zero = mod(find(p_3), floor(1/eps)).*4./floor(1/eps); non_zero = sort(non_zero); zero = find(~p_3); disp(non_zero) end %% functions function t = T(a, b, x, y) t = [1-a.*x.^2.+y, b.*x]; end function res = Tn(a, b, x, y, n) res = [x, y]; for i=1:n res = T(a, b, res(1), res(2)); end end function is_3_periodic = check_3_period(a, b, x, y, eps) T3 = Tn(a, b, x, y, 3); if (T3(1)-x).^2+(T3(2)-y).^2<eps is_3_periodic = 1; else is_3_periodic = 0; end end
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