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

Dmitry Kleinbock; Jinpeng An; Lifan Guan

arxiv: 1501.05409 · v3 · pith:KYOUHDYLnew · submitted 2015-01-22 · 🧮 math.DS

Bounded orbits of diagonalizable flows on rm{SL}₃(mathbb{R})/rm{SL}₃(mathbb{Z})

Jinpeng An , Lifan Guan , Dmitry Kleinbock This is my paper

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keywords mathbbboundeddiagonalizablelambdaorbitscountablydimensionflows

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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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Bounded orbits of diagonalizable flows on rm{SL}₃(mathbb{R})/rm{SL}₃(mathbb{Z})

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