Feigenbaum universal transition of a dynamical system (like the logistic map) to chaotic behaviour through period-doubling cascade involves the functional equation $$g(x)=-\frac1\lambda g(g(\lambda x)$$ x))$$with the boundary conditions$$g(0)=1,\qquad g'(0)=0,\qquad g''(0)<0.$$The parameter \lambda for which a solution exists near x=0 is the inverse of the Feigenbaum constant. 1 Feigenbaum universal transition of a dynamical system (like the logistic map) to chaotic behaviour through period-doubling cascade involves the functional equation$$g(x)=-\frac1\lambda g(g(\lambda x)$$with the boundary conditions$$g(0)=1,\qquad g'(0)=0,\qquad g''(0)<0. The parameter $\lambda$ for which a solution exists near $x=0$ is the inverse of the Feigenbaum constant.