{"paper":{"title":"Examples of type ${\\rm III}_{1}$ inhomogenous Markov shifts supported on topological Markov shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Zemer Kosloff","submitted_at":"2016-02-26T14:14:45Z","abstract_excerpt":"We construct inhomogenous Markov measures for which the shift is of Kreiger type ${\\rm III}_{1}$. These measures are fully supported on a toplogical markov shift space of the hyperbolic toral automorphism $f(x,y)=\\left(\\{x+y\\},x\\right):\\mathbb{T}^{2}\\to\\mathbb{T}^{2}$ and are used in a subsequent paper in the construction of $C^{1}$ Anosov diffeomorphisms of $\\mathbb{T}^{2}$ without an absolutely continuous invariant measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08331","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}