The twisted baker map

Yoshitaka Saiki; Hiroki Takahasi; James A. Yorke

doi:10.1088/1361-6544/acb4d3

The twisted baker map

Yoshitaka Saiki, Hiroki Takahasi, James A. Yorke

Department of Mathematics

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

Abstract

As a model to provide a hands-on, elementary understanding of ‘vortex dynamics’, we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set of hyperbolic repelling periodic points with complex conjugate eigenvalues and that without complex conjugate eigenvalues are simultaneously dense in the phase space. We also show that these two sets equidistribute with respect to the normalised Lebesgue measure, in spite of a non-uniformity in their Lyapunov exponents.

Original language	English
Pages (from-to)	1776-1788
Number of pages	13
Journal	Nonlinearity
Volume	36
Issue number	3
DOIs	https://doi.org/10.1088/1361-6544/acb4d3
Publication status	Published - 2023 Mar 1

Keywords

baker map
equidistribution
mixing
periodic point
piecewise linear map

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

Access to Document

10.1088/1361-6544/acb4d3

Cite this

@article{23fe9b6448bf450c82f4d17e89e90435,

title = "The twisted baker map",

abstract = "As a model to provide a hands-on, elementary understanding of {\textquoteleft}vortex dynamics{\textquoteright}, we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set of hyperbolic repelling periodic points with complex conjugate eigenvalues and that without complex conjugate eigenvalues are simultaneously dense in the phase space. We also show that these two sets equidistribute with respect to the normalised Lebesgue measure, in spite of a non-uniformity in their Lyapunov exponents.",

keywords = "baker map, equidistribution, mixing, periodic point, piecewise linear map",

author = "Yoshitaka Saiki and Hiroki Takahasi and Yorke, {James A.}",

note = "Funding Information: We thank anonymous referees for their careful readings of the manuscript and giving useful comments. This research was supported by the JSPS KAKENHI 19KK0067, 19K21835, 20H01811 and JSPS JPJSBP 120229913. Publisher Copyright: {\textcopyright} 2023 IOP Publishing Ltd & London Mathematical Society.",

year = "2023",

month = mar,

day = "1",

doi = "10.1088/1361-6544/acb4d3",

language = "English",

volume = "36",

pages = "1776--1788",

journal = "Nonlinearity",

issn = "0951-7715",

publisher = "IOP Publishing Ltd.",

number = "3",

}

TY - JOUR

T1 - The twisted baker map

AU - Saiki, Yoshitaka

AU - Takahasi, Hiroki

AU - Yorke, James A.

N1 - Funding Information: We thank anonymous referees for their careful readings of the manuscript and giving useful comments. This research was supported by the JSPS KAKENHI 19KK0067, 19K21835, 20H01811 and JSPS JPJSBP 120229913. Publisher Copyright: © 2023 IOP Publishing Ltd & London Mathematical Society.

PY - 2023/3/1

Y1 - 2023/3/1

N2 - As a model to provide a hands-on, elementary understanding of ‘vortex dynamics’, we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set of hyperbolic repelling periodic points with complex conjugate eigenvalues and that without complex conjugate eigenvalues are simultaneously dense in the phase space. We also show that these two sets equidistribute with respect to the normalised Lebesgue measure, in spite of a non-uniformity in their Lyapunov exponents.

AB - As a model to provide a hands-on, elementary understanding of ‘vortex dynamics’, we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set of hyperbolic repelling periodic points with complex conjugate eigenvalues and that without complex conjugate eigenvalues are simultaneously dense in the phase space. We also show that these two sets equidistribute with respect to the normalised Lebesgue measure, in spite of a non-uniformity in their Lyapunov exponents.

KW - baker map

KW - equidistribution

KW - mixing

KW - periodic point

KW - piecewise linear map

UR - http://www.scopus.com/inward/record.url?scp=85147811252&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85147811252&partnerID=8YFLogxK

U2 - 10.1088/1361-6544/acb4d3

DO - 10.1088/1361-6544/acb4d3

M3 - Article

AN - SCOPUS:85147811252

SN - 0951-7715

VL - 36

SP - 1776

EP - 1788

JO - Nonlinearity

JF - Nonlinearity

IS - 3

ER -

The twisted baker map

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this