QUANTIZATION COEFFICIENTS FOR ERGODIC MEASURES ON INFINITE SYMBOLIC SPACE

摘要

In this paper we consider an ergodic measure with bounded distortion on a symbolic space generated by an infinite alphabet, and showed that for each r ∈ (0, +∞) there exists a unique κ_r ∈ (0, +∞) such that both the κ_r-dimensional lower and upper quantization coefficients for its image measure m with the support lying on the limit set generated by an infinite conformal iterated function system satisfying the strong open set condition are finite and positive. In addition, it shows that κ_r can be expressed by a simple formula involving the temperature function of the system. The result extends and generalizes a similar result of Roychowdhury established for a finite conformal iterated function system [Bull. Polish Acad. Sci. Math. 57 (2009)].