中科院数学与系统科学研究院
数学研究所
学术报告
动力系统研讨班
报告人：Andreas Wieser (Hebrew University of Jerusalem)
题 目：Birkhoff genericity for points on curves in expanding horospheres and Diophantine applications
时 间：2022.11.10（星期四）16:00-17:00
地 点：Zoom ID: 630 5360 7175
摘 要：Let {a(t):t∈
} be a diagonalizable subgroup of SL(d,) for which the expanded horosphere $U$ is abelian. By the Birkhoff ergodic theorem, for any point SL(d,) / SL(d,
) and almost every u∈U the point ux is Birkhoff generic for the flow a(t). One may ask whether the same is true when the points in U are sampled with respect to a measure singular to the Lebesgue measure. In this talk, we discuss work with Omri Solan proving that almost every point on an analytic curve within U is Birkhoff generic when the curve satisfies a non-degeneracy condition.
This Birkhoff genericity result has various applications in Diophantine approximation. In this talk, we shall use Lagarias' notion of best approximations of vectors as an entry point to the topic. No preliminary knowledge of any of the above notions is assumed.
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