Bounded orbits of diagonalizable flows on \rmSL₃(ℝ)/\rmSL₃(ℤ)

2015/01/22 by Jinpeng An, Lifan Guan, An, Jinpeng +3
Mathematics · #11J13 #37A17 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1501.05409

openalex publication_date 2015/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for any countably many one-parameter diagonalizable subgroups F_n of \rmSL₃(ℝ), the set of Λ∈\rmSL₃(ℝ)/\rmSL₃(ℤ) such that all the orbits F_nΛ are bounded has full Hausdorff dimension.

Citations

• Badly approximable points on planar curves and winning

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