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

preprint2015arXivOpen access

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

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

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Bounded orbits of diagonalizable flows on SL3(R)/SL3(Z)\rm{SL}_3(\mathbb{R})/\rm{SL}_3(\mathbb{Z})SL3​(R)/SL3​(Z)

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