On the coordinate functions of peano curves

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On the coordinate functions of peano curves. / Makarov, B. M.; Podkorytov, A. N.

In: St. Petersburg Mathematical Journal, Vol. 28, No. 1, 01.01.2017, p. 115-125.

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

Author

Makarov, B. M. ; Podkorytov, A. N. / On the coordinate functions of peano curves. In: St. Petersburg Mathematical Journal. 2017 ; Vol. 28, No. 1. pp. 115-125.

BibTeX

@article{afb9172e1c65472b970a98eeefd0ba0a,

title = "On the coordinate functions of peano curves",

abstract = "A construction of {"}nonsymmetric{"} plane Peano curves is described whose coordinate functions satisfy the Lipschitz conditions of orders a and 1 - α for some α. It is proved that these curves are metric isomorphisms between the interval [0,1] and the square [0,1]2. This fact is used to show that the graphs of their coordinate functions have the maximum possible Hausdorff dimension for a given smoothness.",

keywords = "Hausdorff dimension, Lipschitz condition, Peano curve",

author = "Makarov, {B. M.} and Podkorytov, {A. N.}",

year = "2017",

month = jan,

day = "1",

doi = "10.1090/spmj/1441",

language = "English",

volume = "28",

pages = "115--125",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "1",

}

RIS

TY - JOUR

T1 - On the coordinate functions of peano curves

AU - Makarov, B. M.

AU - Podkorytov, A. N.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - A construction of "nonsymmetric" plane Peano curves is described whose coordinate functions satisfy the Lipschitz conditions of orders a and 1 - α for some α. It is proved that these curves are metric isomorphisms between the interval [0,1] and the square [0,1]2. This fact is used to show that the graphs of their coordinate functions have the maximum possible Hausdorff dimension for a given smoothness.

AB - A construction of "nonsymmetric" plane Peano curves is described whose coordinate functions satisfy the Lipschitz conditions of orders a and 1 - α for some α. It is proved that these curves are metric isomorphisms between the interval [0,1] and the square [0,1]2. This fact is used to show that the graphs of their coordinate functions have the maximum possible Hausdorff dimension for a given smoothness.

KW - Hausdorff dimension

KW - Lipschitz condition

KW - Peano curve

UR - http://www.scopus.com/inward/record.url?scp=85010471371&partnerID=8YFLogxK

U2 - 10.1090/spmj/1441

DO - 10.1090/spmj/1441

M3 - Article

AN - SCOPUS:85010471371

VL - 28

SP - 115

EP - 125

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 1

ER -

ID: 48414233