Diophantine exponents of measures: a dynamical approach

Dmitry Kleinbock

Diophantine exponents of measures: a dynamical approach

Number Theory 2007-05-23 v1 Dynamical Systems

Authors: Dmitry Kleinbock

Abstract

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.

Keywords

diophantine approximation metric spaces mean dimension

Cite

@article{arxiv.math/0506512,
  title  = {Diophantine exponents of measures: a dynamical approach},
  author = {Dmitry Kleinbock},
  journal= {arXiv preprint arXiv:math/0506512},
  year   = {2007}
}

Comments

AMSTeX, 12 pages

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