d-continuity for countable state shifts

2023/04/12 by Jasmine Bhullar, Bhullar, Jasmine
Computer Science · #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2304.05996

openalex publication_date 2023/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

For full shifts on finite alphabets, Coelho and Quas showed that the map that sends a Hölder continuous potential ϕ to its equilibrium state μ_ϕ is 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.

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