Diophantine exponents of measures: a dynamical approach

Details Diophantine exponents of measures: a dynamical approach Diophantine exponents of measures: a dynamical approach

2005-06-24

arxiv.org/abs/math/0506512v1

Mathematics

Number Theory

AMSTeX, 12 pages

Scientific paper

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 $\Bbb R^n$. 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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