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

Jinpeng An; Anish Ghosh; Lifan Guan; Tue Ly

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

Jinpeng An, Anish Ghosh, Lifan Guan, Tue Ly

Mathematics

Research output: Working paper › Preprint

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.

Original language	English
Publication status	Published - 20 Mar 2018

Keywords

math.DS
math.NT

Access to Document

1611.06470v2Other version, 213 KB

https://arxiv.org/abs/1611.06470

Cite this

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N2 - 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.

AB - 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.

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