Expanding translates of curves and Dirichlet-Minkowski theorem on linear forms

DOI10.1090/S0894-0347-09-00657-2zbMath1200.11055arXiv0804.1424MaRDI QIDQ3584356

Nimish A. Shah

Publication date: 27 August 2010

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.1424

zbMATH Keywords

geometry of numbersDirichlet's theoremDiophantine approximationsRatner's theoremFlow on homogeneous space

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Metric theory (11J83)

Related Items (17)

An `almost all versus no' dichotomy in homogeneous dynamics and Diophantine approximation ⋮ Equidistribution of expanding translates of curves and Diophantine approximation on matrices ⋮ A measure estimate in geometry of numbers and improvements to Dirichlet's theorem ⋮ Equidistribution of curves in homogeneous spaces and Dirichlet's approximation theorem for matrices ⋮ Pointwise equidistribution for one parameter diagonalizable group action on homogeneous space ⋮ Effective equidistribution for multiplicative Diophantine approximation on lines ⋮ A zero-one law for improvements to Dirichlet’s Theorem ⋮ Bounded and divergent trajectories and expanding curves on homogeneous spaces ⋮ Expanding curves in \(\mathrm T^{1}(\mathbb H^{n})\) under geodesic flow and equidistribution in homogeneous spaces ⋮ Universal hitting time statistics for integrable flows ⋮ METRIC DIOPHANTINE APPROXIMATION FOR SYSTEMS OF LINEAR FORMS VIA DYNAMICS ⋮ Invariant measures for solvable groups and Diophantine approximation ⋮ An inhomogeneous Dirichlet theorem via shrinking targets ⋮ The Erdős-Szüsz-Turán distribution for equivariant processes ⋮ Hausdorff dimension and uniform exponents in dimension two ⋮ Equidistribution of expanding translates of curves in homogeneous spaces with the action of \((\mathrm{SO}(n, 1))^k\) ⋮ An effective Ratner equidistribution result for SL\((2,\mathbb R)\ltimes \mathbb R^2\)

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