Flows on homogeneous spaces and Diophantine properties of matrices.

DOI10.1215/S0012-7094-98-09503-5zbMath1115.11311OpenAlexW1483071435MaRDI QIDQ1974862

Dmitry Kleinbock

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-98-09503-5

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Simultaneous homogeneous approximation, linear forms (11J13) Stability theory for smooth dynamical systems (37C75)

Related Items (20)

Singular vectors on manifolds and fractals ⋮ Modified Schmidt games and Diophantine approximation with weights ⋮ A measure estimate in geometry of numbers and improvements to Dirichlet's theorem ⋮ Badly approximable points on manifolds ⋮ Dimension estimates for the set of points with non-dense orbit in homogeneous spaces ⋮ Expanding measures: Random walks and rigidity on homogeneous spaces ⋮ Badly approximable systems of affine forms ⋮ Bounded orbits of certain diagonalizable flows on $SL_{n}(R)/SL_{n}(Z)$ ⋮ Diophantine approximation on matrices and Lie groups ⋮ The topological entropy of non-dense orbits and generalized Schmidt games ⋮ Pointwise equidistribution with an error rate and with respect to unbounded functions ⋮ Quantitative ergodic theorems and their number-theoretic applications ⋮ Invariant measures for solvable groups and Diophantine approximation ⋮ \(\mathbf{Bad(w)}\) is hyperplane absolute winning ⋮ Metric Diophantine approximation with congruence conditions ⋮ Badly approximable points on manifolds and unipotent orbits in homogeneous spaces ⋮ Bounded orbits of diagonalizable flows on finite volume quotients of products of \(\mathrm{SL}_2(\mathbb{R})\) ⋮ Winning property of badly approximable points on curves ⋮ 2-dimensional badly approximable vectors and Schmidt's game ⋮ Badly approximable vectors on fractals

Cites Work

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• Bounded orbits of flows on homogeneous spaces
• Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics
• Diophantine approximation
• Badly approximable systems of linear forms
• A Metrical Theorem in Diophantine Approximation
• Divergent trajectories of flows on homogeneous spaces and Diophantine approximation.
• Ergodicity of Flows on Homogeneous Spaces
• On Badly Approximable Numbers and Certain Games

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