Homogeneous orbit closures and applications (Q2908158)
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scientific article; zbMATH DE number 6076552
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Homogeneous orbit closures and applications |
scientific article; zbMATH DE number 6076552 |
Statements
Homogeneous orbit closures and applications (English)
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4 September 2012
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homogeneous spaces
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orbit closures
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Diophantine approximation
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For \(d\geq 3\), let \(X_d = SL_d(\mathbb Z)\backslash SL_d(\mathbb R)\) and \(A\) be the group of diagonal elements in \(SL_d(\mathbb R)\) with nonnegative entries. By a famous conjecture of Margulis, every bounded \(A\)-orbit in \(X_d\) is expected to be periodic. The authors provide explicit constructions of new examples of \(A\)-regular points of periodic type as well as of \(A\)-irregular points. Moreover, they provide applications to Diophantine approximations of algebraic numbers.
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