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

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DatePublished - 20 Mar 2018
Original languageEnglish

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.

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  • math.DS, math.NT

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