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math.DS1998★ 153 cited
Logarithm laws for flows on homogeneous spaces
D. Y. Kleinbock, G. A. Margulis
We prove that almost all geodesics on a noncompact locally symmetric space of finite volume grow with a logarithmic speed -- the higher rank generalization of a theorem of D. Sulli…
math.NT1998
Flows on homogeneous spaces and Diophantine approximation on manifolds
Dmitry Kleinbock, Gregory Margulis
We present a new approach to metric Diophantine approximation on manifolds based on the correspondence between approximation properties of numbers and orbit properties of certain f…
math.NT1998
Badly approximable systems of affine forms
Dmitry Kleinbock
We prove an inhomogeneous analogue of W. M. Schmidt's (1969) theorem on Hausdorff dimension of the set of badly approximable systems of linear forms. The proof is based on ideas an…