I am wondering if the sign of the Lyapunov exponent is a sufficient condition for chaotic orbits.
Consider the unimodal map $$x_{k+1}=ax_k-x_k^2 \qquad 0<a<4, \quad x_k\geq 0.$$ We define the Lyapunov exponent as, $$\lambda(x_0)=\lim_{n\to\infty}\frac{1}{n}\sum_{i=0}^{n-1}\log|f'(x_i)|$$ for each iteration $n$. For the above map for $x_0=3$ and $a=4$, we can show that $\lambda(3)=\log(2)>0$. Is this a sufficient condition that no chaotic orbits occur for these parameter values of this map?