Product of two Kochergin ows with different exponents is not standard

Adam Kanigowski; Daren Wei

doi:10.4064/sm170218-28-8

Product of two Kochergin ows with different exponents is not standard

Adam Kanigowski, Daren Wei

Mathematics

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

6 Scopus citations

Abstract

We study the standard (zero entropy loosely Bernoulli or loosely Kronecker) property for products of Kochergin smooth ows on T² with one singularity. These ows can be represented as special ows over irrational rotations of the circle and under roof functions which are smooth on T² \ {0} with a singularity at 0. We show that there exists a full measure set D ⊂ T such that the product system of two Kochergin flows with different powers of singularities and rotations from D is not standard.

Original language	English (US)
Pages (from-to)	265-283
Number of pages	19
Journal	Studia Mathematica
Volume	244
Issue number	3
DOIs	https://doi.org/10.4064/sm170218-28-8
State	Published - Jan 2019

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.4064/sm170218-28-8

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title = "Product of two Kochergin ows with different exponents is not standard",

abstract = "We study the standard (zero entropy loosely Bernoulli or loosely Kronecker) property for products of Kochergin smooth ows on T2 with one singularity. These ows can be represented as special ows over irrational rotations of the circle and under roof functions which are smooth on T2 \ {0} with a singularity at 0. We show that there exists a full measure set D ⊂ T such that the product system of two Kochergin flows with different powers of singularities and rotations from D is not standard.",

author = "Adam Kanigowski and Daren Wei",

note = "Funding Information: The authors would like to thank Anatole Katok for his patience, help, encouragement and deep insight. The authors would also like to thank Jean-Paul Thouvenot for several discussions on the subject. The authors would also like to thank for the anonymous referee's many helpful suggestions which improve the article's quality a lot. D. W. was partially supported by the NSF grant DMS-16-02409. Publisher Copyright: {\textcopyright} Instytut Matematyczny PAN, 2019.",

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AU - Kanigowski, Adam

AU - Wei, Daren

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N2 - We study the standard (zero entropy loosely Bernoulli or loosely Kronecker) property for products of Kochergin smooth ows on T2 with one singularity. These ows can be represented as special ows over irrational rotations of the circle and under roof functions which are smooth on T2 \ {0} with a singularity at 0. We show that there exists a full measure set D ⊂ T such that the product system of two Kochergin flows with different powers of singularities and rotations from D is not standard.

AB - We study the standard (zero entropy loosely Bernoulli or loosely Kronecker) property for products of Kochergin smooth ows on T2 with one singularity. These ows can be represented as special ows over irrational rotations of the circle and under roof functions which are smooth on T2 \ {0} with a singularity at 0. We show that there exists a full measure set D ⊂ T such that the product system of two Kochergin flows with different powers of singularities and rotations from D is not standard.

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Product of two Kochergin ows with different exponents is not standard

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