An `almost all versus no' dichotomy in homogeneous dynamics and Diophantine approximation

DOI10.1007/s10711-010-9477-8zbMath1223.37005arXiv0904.1614OpenAlexW1970380314MaRDI QIDQ605075

Dmitry Kleinbock

Publication date: 23 November 2010

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.1614

zbMATH Keywords

Diophantine approximationanalytic submanifoldquantitative non-divergence

Mathematics Subject Classification ID

Related Items (10)

Diophantine approximation on quadrics ⋮ The inhomogeneous Sprindžhuk conjecture over a local field of positive characteristic ⋮ On badly approximable subspaces ⋮ Diophantine approximation on matrices and Lie groups ⋮ Diophantine exponents and the Khintchine Groshev theorem ⋮ Invariant measures for solvable groups and Diophantine approximation ⋮ Multiplicative p-adic metric Diophantine approximation on manifolds and dichotomy of exponents ⋮ A proof of the matrix version of Baker's conjecture in Diophantine approximation ⋮ On metric Diophantine approximation in matrices and Lie groups ⋮ Non-planarity and metric Diophantine approximation for systems of linear forms

Cites Work

• Unnamed Item
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• Badly approximable vectors on fractals
• Equidistribution of expanding translates of curves and Dirichlet's theorem on Diophantine approximation
• Dirichlet's theorem on Diophantine approximation and homogeneous flows
• Simultaneous Diophantine approximation with quadratic and linear forms
• Diophantine exponents of affine subspaces: the simultaneous approximation case
• Limit distributions of expanding translates of certain orbits on homogeneous spaces
• Diophantine approximation
• Flows on homogeneous spaces and Diophantine approximation on manifolds
• Über das Mass der Menge aller \(S\)-Zahlen
• On fractal measures and Diophantine approximation
• Logarithm laws for flows on homogeneous spaces
• Divergent trajectories on noncompact parameter spaces
• Diophantine vectors in analytic submanifolds of Euclidean spaces
• Extremal subspaces and their submanifolds
• An extension of quantitative nondivergence and applications to Diophantine exponents
• Expanding translates of curves and Dirichlet-Minkowski theorem on linear forms
• Divergent trajectories of flows on homogeneous spaces and Diophantine approximation.
• ACHIEVEMENTS AND PROBLEMS IN DIOPHANTINE APPROXIMATION THEORY
• METRIC DIOPHANTINE APPROXIMATION FOR SYSTEMS OF LINEAR FORMS VIA DYNAMICS
• Dirichlet's theorem on diophantine approximation. II

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