Consider the set of irrational numbers between $-1$ and $1$ and call it $T$. Let $4>v>1$ and consider the iterations $ x_0$ belongs to $T$. $$ z_0 = x_0 $$ $$z_{n+1} = v z_n ^5 - (v-1) z_n $$ Let $[a,b]$ be a non-empty open interval where $-1 < a < b < 1$. There exists a largest possible val...