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Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation

Shi, Ronggang
http://rave.ohiolink.edu/etdc/view?acc_num=osu1242259439

Abstract Details

2009, Doctor of Philosophy, Ohio State University, Mathematics.
We consider improvements of Dirichlet’s Theorem on space of matrices $M_{m,n}(R)$. It is shown that for a certain class of fractals $Ksubset [0,1]^{mn}subset M_{m,n}(R)$ of local maximal dimension Dirichlet’s Theorem cannot be improved almost everywhere. This is shown using entropy and dynamics on homogeneous spaces of Lie groups.
Manfred Einsiedler (Advisor)
Vitaly Bergelson (Committee Member)
James Cogdell (Committee Member)
102 p.
Mathematics
Ergodic theory; entropy; Dirichlet's theorem

Recommended Citations

Citations

  • Shi, R. (2009). Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1242259439

    APA Style (7th edition)

  • Shi, Ronggang. Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation. 2009. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1242259439.

    MLA Style (8th edition)

  • Shi, Ronggang. "Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation." Doctoral dissertation, Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1242259439

    Chicago Manual of Style (17th edition)

osu1242259439
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This open access ETD is published by The Ohio State University and OhioLINK.