arXiv subjects
Publications and source records attributed to W. G. Sullivan.
We give a necessary and sufficient condition on beta of the natural extension of a beta-shift, so that any equilibrium measure for a function of bounded total oscillations is a weak Gibbs measure.
For a large class of irreducible shift spaces $X\subset\tA^{\Z^d}$, with $\tA$ a finite alphabet, and for absolutely summable potentials $Φ$, we prove that equilibrium measures for $Φ$ are weak Gibbs measures. In particular, for $d=1$, the result holds for irreducible sofic shifts.