  We study the weak closure $L$ of powers $T^k$ of the non-singular Chacon
transformation $T$ with 2-cuts. This is still an open question does $L$ contain
any Markov operator except an orthogonal projector to the constants $\Theta$
and some polynomials $P(T)$? In this paper we calculate a particular set of
limit polynomials $P_m(T) = \lim_{n \to \infty} T^{-mh_n}$, where $m$ is a
fixed integer number and $h_n = (3^n-1)/2$ are the sequence of heights of
towers in a standard rank one representation of the Chacon map. We show that
for any $d \ge 2$ the family of limit polynomials contains infinitely many
distinct polynomials of degree $d$. We also formulate hyposeses and open
questions concerning the sequence $P_m$ and the entire set $L$.
