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Chebyshevskii Sbornik, 2013, Volume 14, Issue 4, Pages 38–79 (Mi cheb304)  
Badly approximable matrices and Diophantine exponents

O. N. German

M. V. Lomonosov Moscow State University
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Abstract: This paper is a survey of results concerning different kinds of Diophantine exponents. Special attention is paid to the transference principle and to generalization of the concept of badly approximable numbers to matrices and lattices.
Keywords: Diophantine exponents, transference principle, badly approximable matrices, multidimensional continued fractions, Klein polyhedra, dual lattices.
Received: 26.11.2013
English version:
Doklady Mathematics (Supplementary issues), 2022, Volume 106, Issue 2, Pages 201–220
DOI: https://doi.org/10.1134/S106456242270017X
Document Type: Article
UDC: 511.4
Language: Russian
Citation: O. N. German, “Badly approximable matrices and Diophantine exponents”, Chebyshevskii Sb., 14:4 (2013), 38–79; Doklady Mathematics (Supplementary issues), 106:2 (2022), 201–220
Citation in format AMSBIB
\Bibitem{Ger13}
\by O.~N.~German
\paper Badly approximable matrices and Diophantine exponents
\jour Chebyshevskii Sb.
\yr 2013
\vol 14
\issue 4
\pages 38--79
\mathnet{http://mi.mathnet.ru/cheb304}
\transl
\jour Doklady Mathematics (Supplementary issues)
\yr 2022
\vol 106
\issue 2
\pages 201--220
\crossref{https://doi.org/10.1134/S106456242270017X}
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    Full-text PDF :134
    References:59
    First page:1
     
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