**Edit:** I revise the question according to the comment of Gabe Conant.

What is an example of a non constant entire function $f:\mathbb{C}\to \mathbb{C}$ which satisfy the following?:

For every $z\in \mathbb{C}$, the sequence $z,f(z),f^2(z),\ldots,f^n(z),\ldots$ is a bounded sequence but $f$ is not in the form $f(z)=\lambda z,\; |\lambda|\leq 1$.