Abstract
We give sufficient conditions for a shift space (Σ, σ) to be intrinsically ergodic, along with sufficient conditions for every subshift factor of Σ to be intrinsically ergodic. As an application, we show that every subshift factor of a β-shift is intrinsically ergodic, which answers an open question included in Mike Boyle’s article “Open problems in symbolic dynamics”. We obtain the same result for S-gap shifts, and describe an application of our conditions to more general coded systems. One novelty of our approach is the introduction of a new version of the specification property that is well adapted to the study of symbolic spaces with a non-uniform structure.
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D. T. is supported by NSF grant DMS-1101576.
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Climenhaga, V., Thompson, D.J. Intrinsic ergodicity beyond specification: β-shifts, S-gap shifts, and their factors. Isr. J. Math. 192, 785–817 (2012). https://doi.org/10.1007/s11856-012-0052-x
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DOI: https://doi.org/10.1007/s11856-012-0052-x