Bounded orbits of diagonalizable flows on ${\mathrm{SL}}_3(\mathbb{R})/{\mathrm{SL}}_3(\mathbb{Z})$

Abstract

We prove that for any countably many one-parameter diagonalizable subgroups $F_n$ of ${\mathrm{SL}}_3(\mathbb{R})$, the set of $\Lambda \in {\mathrm{SL}}_3(\mathbb{R})/{\mathrm{SL}}_3(\mathbb{Z})$ such that all the orbits $F_n\Lambda$ are bounded has full Hausdorff dimension.

21 pages. Added references and expanded the last section

References in corpus (1)

• Badly approximable points on planar curves and winning