Birkhoff generic points on curves in horospheres

Omri Nisan Solan, Andreas Wieser

Let $\{a_t:t\in \mathbb{R}\}<S{L}_d(\mathbb{R})$ be a diagonalizable subgroup whose expanding horospherical subgroup $U<S{L}_d(\mathbb{R})$ is abelian. By the Birkhoff ergodic…