No CrossRef data available.
Published online by Cambridge University Press: 03 October 2025
For full shifts on finite alphabets, Coelho and Quas [Criteria for $\overline {d}$-continuity. Trans. Amer. Math. Soc. 350(8) (1998), 3257–3268] showed that the map that sends a Hölder continuous potential
$\phi $ to its equilibrium state
$\mu _\phi $ is
$\overline {d}$-continuous. We extend this result to the setting of full shifts on countable (infinite) alphabets. As part of the proof, we show that the map that sends a strongly positive recurrent potential to its normalization is continuous for potentials on mixing countable state Markov shifts.