Square summability of variations and convergence of the transfer operator

Details Square summability of variations and convergence of the transfer operator Square summability of variations and convergence of the transfer operator

2006-12-05

arxiv.org/abs/math/0612131v1

Mathematics

Dynamical Systems

8 pages

Scientific paper

In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [13], we prove that the sequence of iterates of the transfer operator converges under square summability of variations of the g-function, a condition which gave uniqueness of a g-measure in [7]. We also prove uniqueness of so-called G-measures, introduced by Brown and Dooley [2], under square summability of variations.

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