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arXiv · 1011.2780

Intrinsic ergodicity beyond specification: beta-shifts, S-gap shifts, and their factors

Vaughn Climenhaga·Daniel J. Thompson
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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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Vaughn Climenhaga, Daniel J. Thompson. 2011-06-17. Intrinsic ergodicity beyond specification: beta-shifts, S-gap shifts, and their factors. https://doi.org/10.1007/s11856-012-0052-x

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