Several Questions and Hypotheses Concerning Limit Polynomials for the Chacon Transformation (3)

We study the weak closure L = WCl({Tˆk}) of powers of non- singular Chacon transformation with 2-cuts. It is still an open question does L contain any Markov operator except an orthogonal projector to the constants Θ and some polynomials P (Tˆ) ? In this paper we calculate a particular set of limit polynomials P m(Tˆ) = lim Tˆ−mhn , m ∈ Z, n→∞ where h n = (3n − 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 ≥ 2 the family of limit polynomials contains infinitely many polynomials of degree d. We also formulate hypotheses and open questions concerning the sequence of polynomials P m and the entire set L .