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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 275, Pages 87–98 (Mi tm3341)  
This article is cited in 9 scientific papers (total in 9 papers)

The family of bi-Lipschitz classes of Delone sets in Euclidean space has the cardinality of the continuum

A. N. Magazinov

M. V. Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (204 kB) Citations (9)
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Abstract: It is proved that the family of bi-Lipschitz classes of Delone sets in Euclidean space of dimension at least 2 has the cardinality of the continuum.
Received in May 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2011, Volume 275, Pages 78–89
DOI: https://doi.org/10.1134/S0081543811080050
Bibliographic databases:
Document Type: Article
UDC: 514.12
Language: Russian
Citation: A. N. Magazinov, “The family of bi-Lipschitz classes of Delone sets in Euclidean space has the cardinality of the continuum”, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth, Trudy Mat. Inst. Steklova, 275, MAIK Nauka/Interperiodica, Moscow, 2011, 87–98; Proc. Steklov Inst. Math., 275 (2011), 78–89
Citation in format AMSBIB
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\paper The family of bi-Lipschitz classes of Delone sets in Euclidean space has the cardinality of the continuum
\inbook Classical and modern mathematics in the wake of Boris Nikolaevich Delone
\bookinfo Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth
\serial Trudy Mat. Inst. Steklova
\yr 2011
\vol 275
\pages 87--98
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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Linking options:
  • https://www.mathnet.ru/eng/tm3341
  • https://www.mathnet.ru/eng/tm/v275/p87
    • This publication is cited in the following 9 articles:
    1. Michael Dymond, Vojtěch Kaluža, “Divergence of separated nets with respect to displacement equivalence”, Geom Dedicata, 218:1 (2024)  crossref
    2. Michael Dymond, Vojtěch Kaluža, “Highly irregular separated nets”, Isr. J. Math., 253:2 (2023), 501  crossref
    3. Smilansky Y., Solomon Ya., “A Dichotomy For Bounded Displacement Equivalence of Delone Sets”, Ergod. Theory Dyn. Syst., 42:8 (2022), 2693–2710  crossref  isi  scopus
    4. Yotam Smilansky, Yaar Solomon, “Discrepancy and rectifiability of almost linearly repetitive Delone sets”, Nonlinearity, 35:12 (2022), 6204  crossref
    5. Frettloeh D., Smilansky Y., Solomon Ya., “Bounded Displacement Non-Equivalence Insubstitution Tilings”, J. Comb. Theory Ser. A, 177 (2021), 105326  crossref  mathscinet  isi
    6. Solomon Ya., “Continuously Many Bounded Displacement Non-Equivalences in Substitution Tiling Spaces”, J. Math. Anal. Appl., 492:1 (2020), 124426  crossref  mathscinet  isi
    7. Dymond M., Kaluza V., Kopecka E., “Mapping N Grid Points Onto a Square Forces An Arbitrarily Large Lipschitz Constant”, Geom. Funct. Anal., 28:3 (2018), 589–644  crossref  mathscinet  zmath  isi
    8. Dymarz T., Kelly M., Li S., Lukyanenko A., “Separated Nets in Nilpotent Groups”, Indiana Univ. Math. J., 67:3 (2018), 1143–1183  crossref  mathscinet  isi
    9. Isabel Cortez M., Navas A., “Some examples of repetitive, nonrectifiable Delone sets”, Geom. Topol., 20:4 (2016), 1909–1939  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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