Birkhoff genericity for points on curves in expanded horospheres

Vortrag von Andreas Wieser

Datum: 10.10.22  Zeit: 13.30 - 14.30  Raum: Y27H28

Let \(\{a(t):t \in \mathbb{R}\}\) be a diagonalizable subgroup of \(SL(d,\mathbb{R})\) for which the expanded horosphere \(U\) is abelian. By the Birkhoff ergodic theorem, for any point \(x \in SL(d,\mathbb{R})/SL(d,\mathbb{Z})\) and almost every \(u \in U\) 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.