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Phase transitions in one-dimensional subshifts

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  • In this note we give simple examples of one-dimensional mixing subshift with positive topological entropy which have two distinct measures of maximal entropy. We also give examples of subshifts which have two mutually singular equilibrium states for Hölder continuous functions. We also indicate how the construction can be extended to yield examples with any number of equilibrium states.
    Mathematics Subject Classification: Primary: 37D35; Secondary: 82B26.

    Citation:

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