Asymptotics of entries of products of nonnegative 2-by-2 matrices

Hua-Ming Wang

Let $M$ and $M_n,n\ge 1$ be nonnegative 2-by-2 matrices such that ${\lim }_{n\to \infty }{M}_n=M.$ It is usually hard to estimate the entries of $M_{k+1}\cdots M_{k+n}$ which are u…