Standard

Additive dimension theory for birkhoff curves. / Osipov, Alexander V.; Kovalew, Ivan A.; Serow, Dmitry W.

In: Nonlinear Phenomena in Complex Systems, Vol. 22, No. 2, 2018, p. 164-176.

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

Harvard

Osipov, AV, Kovalew, IA & Serow, DW 2018, 'Additive dimension theory for birkhoff curves', Nonlinear Phenomena in Complex Systems, vol. 22, no. 2, pp. 164-176.

APA

Osipov, A. V., Kovalew, I. A., & Serow, D. W. (2018). Additive dimension theory for birkhoff curves. Nonlinear Phenomena in Complex Systems, 22(2), 164-176.

Vancouver

Osipov AV, Kovalew IA, Serow DW. Additive dimension theory for birkhoff curves. Nonlinear Phenomena in Complex Systems. 2018;22(2):164-176.

Author

Osipov, Alexander V. ; Kovalew, Ivan A. ; Serow, Dmitry W. / Additive dimension theory for birkhoff curves. In: Nonlinear Phenomena in Complex Systems. 2018 ; Vol. 22, No. 2. pp. 164-176.

BibTeX

@article{a4503c50d1224a93aaeebdf36cc7da03,
title = "Additive dimension theory for birkhoff curves",
abstract = "The additive dimension for a common boundary of the Wada basins bases (and Wada ocean) accessible points has been defined. One is constituted to be value being inverse to fractional density for the sequence (basis) zero Schnirelmann density and one characterizes only metric property of the boundary (Birkhoff curve). The additive dimension is similar to Hausdorff–Besicovitch dimension. All Wada basin and Wada ocean are quite metrically characterized to be only additive dimension of accessible points. It follows that additive dimension is invariant with respect to a plane diffeomorphism.",
keywords = "Accessible point, Additive basis, Birkhoff curve, Cantor set, Dissipative dynamic system, Fractional density, Hausdorff–Besicovitch dimension, Indecomposable continuum (atom), Schnirelmann density, Top of umbrella, Wada basins",
author = "Osipov, {Alexander V.} and Kovalew, {Ivan A.} and Serow, {Dmitry W.}",
year = "2018",
language = "English",
volume = "22",
pages = "164--176",
journal = "Nonlinear Phenomena in Complex Systems",
issn = "1561-4085",
publisher = "Белорусский государственный университет",
number = "2",

}

RIS

TY - JOUR

T1 - Additive dimension theory for birkhoff curves

AU - Osipov, Alexander V.

AU - Kovalew, Ivan A.

AU - Serow, Dmitry W.

PY - 2018

Y1 - 2018

N2 - The additive dimension for a common boundary of the Wada basins bases (and Wada ocean) accessible points has been defined. One is constituted to be value being inverse to fractional density for the sequence (basis) zero Schnirelmann density and one characterizes only metric property of the boundary (Birkhoff curve). The additive dimension is similar to Hausdorff–Besicovitch dimension. All Wada basin and Wada ocean are quite metrically characterized to be only additive dimension of accessible points. It follows that additive dimension is invariant with respect to a plane diffeomorphism.

AB - The additive dimension for a common boundary of the Wada basins bases (and Wada ocean) accessible points has been defined. One is constituted to be value being inverse to fractional density for the sequence (basis) zero Schnirelmann density and one characterizes only metric property of the boundary (Birkhoff curve). The additive dimension is similar to Hausdorff–Besicovitch dimension. All Wada basin and Wada ocean are quite metrically characterized to be only additive dimension of accessible points. It follows that additive dimension is invariant with respect to a plane diffeomorphism.

KW - Accessible point

KW - Additive basis

KW - Birkhoff curve

KW - Cantor set

KW - Dissipative dynamic system

KW - Fractional density

KW - Hausdorff–Besicovitch dimension

KW - Indecomposable continuum (atom)

KW - Schnirelmann density

KW - Top of umbrella

KW - Wada basins

UR - http://www.scopus.com/inward/record.url?scp=85071259057&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85071259057

VL - 22

SP - 164

EP - 176

JO - Nonlinear Phenomena in Complex Systems

JF - Nonlinear Phenomena in Complex Systems

SN - 1561-4085

IS - 2

ER -

ID: 51710995