Badly approximable matrices and Diophantine exponents

O. N. German

Čebyševskij sbornik, Tome 14 (2013) no. 4, pp. 38-79.

Résumé

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.

Détail

Keywords: Diophantine exponents, transference principle, badly approximable matrices, multidimensional continued fractions, Klein polyhedra, dual lattices.

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