Bounded orbits of Diagonalizable Flows on finite volume quotients of products of SL₂(ℝ)

2016/11/20 by Jinpeng An, Anish Ghosh, An, Jinpeng +5
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1611.06470

openalex publication_date 2016/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a number field analogue of W. M. Schmidt's conjecture on the intersection of weighted badly approximable vectors and use this to prove an instance of a conjecture of An, Guan and Kleinbock. Namely, let G := SL₂(ℝ) × … × SL₂(ℝ) and Γ be a lattice in G. We show that the set of points on G/Γ whose forward orbits under a one parameter Ad-semisimple subsemigroup of G are bounded, form a hyperplane absolute winning set.

Related

• Bounded orbits of certain diagonalizable flows on SL_n(ℝ)/SL_n(ℤ)
• Hyperplane absolute winning property of bounded orbits under diagonalizable flows on SL₃(ℂ)/SL₃(O_\mathbbK)
• Bounded orbits of diagonalizable flows on \rmSL₃(ℝ)/\rmSL₃(ℤ)
• Dimension drop for diagonalizable flows on homogeneous spaces
• Simultaneously bounded and dense orbits for commuting Cartan actions