Let $F: \mathbb R \to \mathbb R$ be $F(x) = x^3 - \lambda x$ for $\lambda >0$. How to show that if $\lambda$ is sufficiently large, then the set of points which do not tend to infinity is a Cantor set?
In the above question, a point $x \in \mathbb R$ tends to infinity if $F^n (x) \to \infty$, where the power $n$ means $n$ times composition of $F$.
How to write down the set of points which do not tend to infinity by using set notation?