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

Published 22 Jan 2015 in math.DS | (1501.05409v3)

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

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