Correction to 'Local limit theorem and distribution of periodic orbits of Lasota-Yorke transformations with infinite Markov partition'

摘要

First of all, we give a suitable choice of y_J. Let K={K_1,…, K_p} be the finite set of the intervals appearing as T Int J for some J∈P. We note that T~n Int J∈K for any J∈P_n by the Markov property of T. Choose a_j∈K_j for j=1, 2,…, p and we continue our discussion with fixing them. For each J∈P_n, y_J∈J should be chosen so that T~ny_J=a_j if T~n Int J=K_j. Then it is clear that T y_J=y_J, holds whenever J∈P_n, J'∈P_(n-1), and T Int J=Int J'. Thus the present choice of y_J guarantees the validity of (*).