On the Growth Function of -Valued Dynamics.

This paper answers the question of V. M. Buchstaber on the growth function in case of certain -valued group. This question is in close relation to specific discrete integrable systems. In the present paper, we find a specific formula for the growth function in the case of prime . We also prove a polynomial asymptotic estimate of the growth function in the general case. At the end, we pose new conjectures and questions regarding growth functions. [ABSTRACT FROM AUTHOR]