BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dominik Kwietniak (Jagiellonian University) DTSTART:20201002T081500Z DTEND:20201002T094500Z DTSTAMP:20260423T021830Z UID:DSSUJ/9 DESCRIPTION:Title: Db ar-approachability\, entropy density and B-free shifts\nby Dominik Kwi etniak (Jagiellonian University) as part of Dynamical systems seminar at t he Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nWe study which properties of shift spaces transfer to their Hausdorff\nmetric dbar- limits. In particular\, we study shift spaces we call\ndbar-approachable\, which are Hausdorff metric dbar-limits of their own\nk-step Markov approx imations. We provide a topological\ncharacterisation of chain mixing dbar- approachable shift spaces using\nthe dbar-shadowing property. This can be considered as an analogue for\nFriedman and Ornstein's characterisation of Bernoulli processes. We\nprove that many classical specification properti es imply chain mixing\nand dbar-approachability. It follows that there are tons of\ninteresting dbar-approachable shift spaces (mixing shifts of fin ite\ntype\, or more generally mixing sofic shifts\, or even more generally \,\nshift spaces with the specification or beta-shifts. In addition\, we\n construct minimal and proximal examples of dbar-approachable shift\nspaces \, thus proving dbar-approachability is a more general phenomenon\nthan sp ecification. We also show that dbar-approachability and\nchain-mixing impl y dbar-stability\, a property recently introduced by\nTim Austin in his st udy of Bernoulliness of equilibrium states. This\nallows us to provide fir st examples of minimal or proximal dbar-stable\nshift spaces\, thus answer ing a question posed by Austin. Finally\, we\nshow that the set of shift spaces with entropy-dense ergodic measures\nis closed wrt dbar Hausdorff m etric. Note that entropy-density of\nergodic measures is known to hold for many classes of shift spaces\nwith variants of the specification property \, but our result show that\nin these cases the entropy-density is a mere consequence of\nentropy-density of mixing shifts of finite type and\ndbar- approachability. Since we know there are examples of minimal or\nproximal dbar-approachable shifts\, we see that our technique yields\nentropy-densi ty for examples which were beyond the reach of methods\nbased on specifica tion properties. Finally\, we apply our technique to\nhereditary closures of B-free shifts (a class including many\ninteresting B-free shifts). Thes e shift spaces are not chain-mixing\,\nhence they are not dbar-approachabl e\, but they are easily seen to be\napproximated by naturally defined sequ ences of transitive sofic\nshifts\, and this implies entropy-density. This is a joint work with\nJakub Konieczny and Michal Kupsa.\n LOCATION:https://researchseminars.org/talk/DSSUJ/9/ END:VEVENT END:VCALENDAR