Geodesic
Diophantine exponents of measures: a~dynamical approach and submanifolds
Trudy Instituta matematiki, Tome 14 (2006) no. 1, pp. 108-117.

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We place the theory of metric Diophantine approximation on manifolds into a broader context of studying Diophantine properties of points generic with respect to certain measures on $\mathbb R^n$. The correspondence between multidimensional Diophantine approximation and dynamics of lattices in Euclidean spaces is discussed in an elementary way, and several recent results obtained by means of this correspondence are surveyed. 
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D. Kleinbock. Diophantine exponents of measures: a~dynamical approach and submanifolds. Trudy Instituta matematiki, Tome 14 (2006) no. 1, pp. 108-117. http://geodesic.mathdoc.fr/item/TIMB_2006_14_1_a12/