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

Jinpeng An; Lifan Guan; Dmitry Kleinbock

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

Dynamical Systems 2015-02-03 v3

Authors: Jinpeng An , Lifan Guan , Dmitry Kleinbock

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.

Keywords

hausdorff dimension

Cite

@article{arxiv.1501.05409,
  title  = {Bounded orbits of diagonalizable flows on $\rm{SL}_3(\mathbb{R})/\rm{SL}_3(\mathbb{Z})$},
  author = {Jinpeng An and Lifan Guan and Dmitry Kleinbock},
  journal= {arXiv preprint arXiv:1501.05409},
  year   = {2015}
}

Comments

21 pages. Added references and expanded the last section

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