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arXiv · 2605.28957

Existence of Gibbs measures for sequences of continuous functions

Yuki Yayama
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Abstract

We give a necessary and sufficient condition for the existence of invariant Gibbs measures for sequences of continuous functions on one-sided subshifts and, more generally, for the existence of Gibbs measures. These extend the results of Kim [7] and Baker and Ghenciu [2], respectively, to sequences of continuous functions on one-sided subshifts. In particular, we characterize the existence of invariant Gibbs measures for subadditive sequences. For superadditive sequences on subshifts with the strong specification property, such a characterization gives a necessary and sufficient condition for the uniqueness of invariant Gibbs measures. We apply these results to study some problems in the theory of relative pressure and relative equilibrium states.

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Yuki Yayama. 2026-05-27. Existence of Gibbs measures for sequences of continuous functions. https://arxiv.org/abs/2605.28957

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