Counterexamples to double recurrence for non-commuting deterministic transformations

Zemer Kosloff; Shrey Sanadhya

doi:10.48550/arXiv.2507.15528

Counterexamples to double recurrence for non-commuting deterministic transformations

Zemer Kosloff, Shrey Sanadhya

School of Mathematics

Research output: Working paper › Preprint

1 Downloads (Pure)

Abstract

We show that if p₁, p₂ are injective, integer polynomials that vanish at the origin, such that either both are of degree 1 or both are of degree 2 or higher, then double recurrence fails for non-commuting, mixing, zero entropy transformations. This answers a question of Frantzikinakis and Host completely.

Original language	English
Publisher	arXiv.org
DOIs	https://doi.org/10.48550/arXiv.2507.15528
Publication status	Published - 21 Jul 2025

Keywords

math.DS

Access to Document

10.48550/arXiv.2507.15528Licence: CC BY

Full-text PDF (pre-print)Submitted manuscript, 477 KBLicence: CC BY

Handle.net

Persistent link

Cite this

@techreport{b62d76c807e14d7ea6f3faaed2112d01,

title = "Counterexamples to double recurrence for non-commuting deterministic transformations",

abstract = "We show that if p1, p2 are injective, integer polynomials that vanish at the origin, such that either both are of degree 1 or both are of degree 2 or higher, then double recurrence fails for non-commuting, mixing, zero entropy transformations. This answers a question of Frantzikinakis and Host completely.",

keywords = "math.DS",

author = "Zemer Kosloff and Shrey Sanadhya",

year = "2025",

month = jul,

day = "21",

doi = "10.48550/arXiv.2507.15528",

language = "English",

publisher = "arXiv.org",

address = "United Kingdom",

type = "WorkingPaper",

institution = "arXiv.org",

}

TY - UNPB

T1 - Counterexamples to double recurrence for non-commuting deterministic transformations

AU - Kosloff, Zemer

AU - Sanadhya, Shrey

PY - 2025/7/21

Y1 - 2025/7/21

N2 - We show that if p1, p2 are injective, integer polynomials that vanish at the origin, such that either both are of degree 1 or both are of degree 2 or higher, then double recurrence fails for non-commuting, mixing, zero entropy transformations. This answers a question of Frantzikinakis and Host completely.

AB - We show that if p1, p2 are injective, integer polynomials that vanish at the origin, such that either both are of degree 1 or both are of degree 2 or higher, then double recurrence fails for non-commuting, mixing, zero entropy transformations. This answers a question of Frantzikinakis and Host completely.

KW - math.DS

U2 - 10.48550/arXiv.2507.15528

DO - 10.48550/arXiv.2507.15528

M3 - Preprint

BT - Counterexamples to double recurrence for non-commuting deterministic transformations

PB - arXiv.org

ER -

Counterexamples to double recurrence for non-commuting deterministic transformations

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Cite this