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Tr. Mat. Inst. Steklova, 2004, Volume 247, Pages 294–303 (Mi tm27)  

This article is cited in 9 scientific papers (total in 9 papers)

On Fractal Peano Curves

E. V. Shchepin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: It is shown that, for a fractal Peano curve $p(t)$ that maps a unit segment onto a unit square, there always exists a pair of points $t,t'$ of the segment that satisfy the inequality $|p(t)-p(t')|^2\ge 5|t-t'|$. As is clear from the classical Peano–Hilbert curve, the number $5$ in this inequality cannot be replaced by a number greater than $6$ (the result of K. Bauman).

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 247, 272–280

Bibliographic databases:
UDC: 519.6
Received in April 2004

Citation: E. V. Shchepin, “On Fractal Peano Curves”, Geometric topology and set theory, Collected papers. Dedicated to the 100th birthday of professor Lyudmila Vsevolodovna Keldysh, Tr. Mat. Inst. Steklova, 247, Nauka, MAIK Nauka/Inteperiodika, M., 2004, 294–303; Proc. Steklov Inst. Math., 247 (2004), 272–280

Citation in format AMSBIB
\Bibitem{Shc04}
\by E.~V.~Shchepin
\paper On Fractal Peano Curves
\inbook Geometric topology and set theory
\bookinfo Collected papers. Dedicated to the 100th birthday of professor Lyudmila Vsevolodovna Keldysh
\serial Tr. Mat. Inst. Steklova
\yr 2004
\vol 247
\pages 294--303
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm27}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2168180}
\zmath{https://zbmath.org/?q=an:1124.28011}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2004
\vol 247
\pages 272--280


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. E. Bauman, “The dilation factor of the Peano–Hilbert curve”, Math. Notes, 80:5 (2006), 609–620  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. E. V. Shchepin, K. E. Bauman, “Minimal Peano Curve”, Proc. Steklov Inst. Math., 263 (2008), 236–256  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. K. E. Bauman, “One-side Peano curves of fractal genus $9$”, Proc. Steklov Inst. Math., 275 (2011), 47–59  mathnet  crossref  mathscinet  isi  elib  elib
    4. Nosovskii A.M., Larina I.M., “Fraktalnye otnosheniya komponentov zhivogo organizma kak osnova ego sistemnoi tselostnosti (ch. 1)”, Biomeditsinskaya radioelektronika, 2013, no. 3, 026–037  elib
    5. K. E. Bauman, “Lower estimate of the square-to-linear ratio for regular Peano curves”, Discrete Math. Appl., 24:3 (2014), 123–128  mathnet  crossref  crossref  mathscinet  elib  elib
    6. D. K. Shalyga, “O tochnom vychislenii kubo-lineinogo otnosheniya krivykh Peano”, Preprinty IPM im. M. V. Keldysha, 2014, 088, 13 pp.  mathnet
    7. E. V. Shchepin, “Attainment of Maximum Cube-to-Linear Ratio for Three-Dimensional Peano Curves”, Math. Notes, 98:6 (2015), 971–976  mathnet  crossref  crossref  mathscinet  isi  elib
    8. A. A. Korneev, E. V. Shchepin, “$L_\infty $-locality of three-dimensional Peano curves”, Proc. Steklov Inst. Math., 302 (2018), 217–249  mathnet  crossref  crossref  isi  elib
    9. Kauranen A., Koskela P., Zapadinskaya A., “Regularity and Modulus of Continuity of Space-Filling Curves”, J. Anal. Math., 137:1 (2019), 73–100  crossref  isi
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