Let $\{x_n\}$ be a real sequence defined by: $$ x_1=a \\ x_{n+1}=\frac{2x_n^3}{3x_n^2-1} $$
For all $n=1,2,3...$ and $a$ is a real number. Find all $a$ such that $\{x_n\}$ has finite limit when $n\to +\infty$ and find the finite limit in that cases.
I'm stuck when $a\in(-1,1)$ and $a<-1$ Please help me. Thanks