Why is the state variable in Brock-Mirman model bounded above?

as a beginner in macro, I'm trying to understand the Brock-Mirman model for one of my assignments and I am told (in the assignment) that there is a $$k^*$$ such that k is bounded.

From the production function I see that $$\ k_{t+1} = k_t^\alpha$$ will go to a $$k^*$$ as $$t\to\infty$$, and we already know that marginal product of capital will go to zero. But what is the intuition behind this? How does $$k^* = k^*{^\alpha}$$ work as a bound?