On manifolds admitting stable type iii1 anosov diffeomorphisms

Zemer Kosloff

doi:10.3934/JMD.2018020

On manifolds admitting stable type iii₁ anosov diffeomorphisms

Zemer Kosloff

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that for every d ≠ 3 there is an Anosov diffeomorphism of T^d which is of stable Krieger type III₁ (its Maharam extension is weakly mixing). This is done by a construction of stable type III₁ Markov measures on the golden mean shift which can be smoothly realized as a C¹ Anosov diffeomorphism of T² via the construction in our earlier paper.

Original language	English
Pages (from-to)	251-270
Number of pages	20
Journal	Journal of Modern Dynamics
Volume	13
DOIs	https://doi.org/10.3934/JMD.2018020
State	Published - 2018

Keywords

Anosov diffeomorphisms
Maharam exten-sion
Markov shifts
Ratio set

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

Access to Document

10.3934/JMD.2018020

Cite this

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abstract = "We prove that for every d ≠ 3 there is an Anosov diffeomorphism of Td which is of stable Krieger type III1 (its Maharam extension is weakly mixing). This is done by a construction of stable type III1 Markov measures on the golden mean shift which can be smoothly realized as a C1 Anosov diffeomorphism of T2 via the construction in our earlier paper.",

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AB - We prove that for every d ≠ 3 there is an Anosov diffeomorphism of Td which is of stable Krieger type III1 (its Maharam extension is weakly mixing). This is done by a construction of stable type III1 Markov measures on the golden mean shift which can be smoothly realized as a C1 Anosov diffeomorphism of T2 via the construction in our earlier paper.

KW - Anosov diffeomorphisms

KW - Maharam exten-sion

KW - Markov shifts

KW - Ratio set

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