On the coordinate functions of Peano curves
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B. M. Makarov and A. N. Podkorytov
Translated by: N. Tsilevich - St. Petersburg Math. J. 28 (2017), 115-125
- DOI: https://doi.org/10.1090/spmj/1441
- Published electronically: November 30, 2016
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Abstract:
A construction of “nonsymmetric” plane Peano curves is described whose coordinate functions satisfy the Lipschitz conditions of orders $\alpha$ and $1-\alpha$ for some $\alpha$. 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.References
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Bibliographic Information
- B. M. Makarov
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia
- Email: BM1092@gmail.com
- A. N. Podkorytov
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia
- Email: a.podkorytov@gmail.com
- Received by editor(s): September 7, 2015
- Published electronically: November 30, 2016
- © Copyright 2016 American Mathematical Society
- Journal: St. Petersburg Math. J. 28 (2017), 115-125
- MSC (2010): Primary 26A16; Secondary 28A12
- DOI: https://doi.org/10.1090/spmj/1441
- MathSciNet review: 3591069