2010/11/30 by Vaughn Climenhaga, Daniel J. Thompson · 1 citation
Mathematics · #math.DS #msc:37A35 #msc:37B10 #msc:37B40
paper · pdf · doi:10.1007/s11856-012-0052-x
published as Israel J. Math, Vol. 192 (November 2012), Issue 2, pp 785-817 · 27 pages, 1 figure, minor changes based on referee's suggestions, in v.3 the result on coded systems has been moved to the introduction, resulting in small changes to numbering (lettering) of results
arxiv created 2011/06/17 · arxiv updated 2015/03/17
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.