Nimish A. Shah

activity

20242026

collaborators

4 papers

math.DS2026

Birkhoff genericity on affine subspaces in horospheres

Nimish A. Shah, Pengyu Yang

We study Birkhoff genericity for a simple uniformly expanding diagonal flow on $SL_{n + 1} (R) / SL_{n + 1} (Z)$ , with initial points restricted to affine…

math.DS2026

Limit distributions for $SO (n, 1)$ action on $k$ -lattices in $R^{n + 1}$

Michael Bersudsky, Nimish A. Shah

We study the asymptotic distribution of norm ball averages along orbits of a lattice $I^ \subset SO (n, 1)$ acting on the moduli space of pairs of orthogonal discrete subgroups…

math.DS2025

Equidistribution of polynomially bounded o-minimal curves in homogeneous spaces

Michael Bersudsky, Nimish A. Shah, Hao Xing

We extend Ratner's theorem on equidistribution of individual orbits of unipotent flows on finite volume homogeneous spaces of Lie groups to trajectories of non-contracting curves d…

math.DS2024

An effective closing lemma for unipotent flows

Elon Lindenstrauss, Gregory Margulis, Amir Mohammadi +2

We prove an effective closing lemma for unipotent flows on quotients of perfect real groups. This is largely motivated by recent developments in effective unipotent dynamics.

Birkhoff genericity on affine subspaces in horospheres

Limit distributions for SO(n,1) action on k-lattices in Rn+1

Equidistribution of polynomially bounded o-minimal curves in homogeneous spaces

An effective closing lemma for unipotent flows

Limit distributions for $SO (n, 1)$ action on $k$ -lattices in $R^{n + 1}$