Erratum: A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function

摘要

If T : X → X is a two-sided subshift on a finite number of symbols and T : X → X is the corresponding one-sided subshift we give a necessary and sufficient condition for a continuous function f : X → R to be cohomologous, with respect to (X, T), to a continuous function which can be defined on X. The property of being cohomologous to such a 'one-sided' function is important in the study of equilibrium states because there are extra tools, such as the Ruellc transfer operator, for onesided systems. We present the results in the more general context when T : X → X is a continuous surjection of a compact metric space and T : X → X is its natural extension, and look at the special case of subshifts. We also prove some related results and give applications to subshifts.