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arXiv · 1602.08331

Examples of type ${\rm III}_{1}$ inhomogenous Markov shifts supported on topological Markov shifts

Zemer Kosloff
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Abstract

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.

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Zemer Kosloff. 2016-02-26. Examples of type ${\rm III}_{1}$ inhomogenous Markov shifts supported on topological Markov shifts. https://arxiv.org/abs/1602.08331

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