Dynamics of subgroup actions on homogeneous spaces of Lie groups and applications to number theory
D Kleinbock, N Shah, A Starkov - Handbook of dynamical systems, 2002 - Elsevier
Publisher Summary This chapter presents an exposition of homogeneous dynamics—that is,
the dynamical and ergodic properties of actions on the homogeneous spaces of Lie groups …
the dynamical and ergodic properties of actions on the homogeneous spaces of Lie groups …
Dirichlet's theorem on Diophantine approximation and homogeneous flows
D Kleinbock, B Weiss - arXiv preprint math/0612171, 2006 - arxiv.org
We show that for any $\epsilon< 1$ and any $\mathcal {T} $drifting away from walls',
Dirichlet's Theorem cannot be $\epsilon $-improved along $\mathcal {T} $ for Lebesgue …
Dirichlet's Theorem cannot be $\epsilon $-improved along $\mathcal {T} $ for Lebesgue …
[图书][B] Dynamical systems on homogeneous spaces
AN Starkov, AN Starkov - 2000 - cambridge.org
The modern study of dynamical systems on homogeneous spaces has roots in classical
dynamics and classical number theory. For example, the geodesic flow on a surface of …
dynamics and classical number theory. For example, the geodesic flow on a surface of …
Pointwise equidistribution with an error rate and with respect to unbounded functions
D Kleinbock, R Shi, B Weiss - Mathematische Annalen, 2017 - Springer
Abstract Consider G= SL _ d (R) G= SL d (R) and Γ= SL _ d (Z) Γ= SL d (Z). It was recently
shown by the second-named author (Shi, Pointwise equidistribution for one parameter …
shown by the second-named author (Shi, Pointwise equidistribution for one parameter …
Expanding cone and applications to homogeneous dynamics
R Shi - International Mathematics Research Notices, 2021 - academic.oup.com
Let be a horospherical subgroup of a noncompact simple Lie group and let be a maximal
split torus in the normalizer of. We define the expanding cone in with respect to and show …
split torus in the normalizer of. We define the expanding cone in with respect to and show …
Effective equidistribution of translates of maximal horospherical measures in the space of lattices
K Dabbs, M Kelly, H Li - arXiv preprint arXiv:1604.04341, 2016 - arxiv.org
Recently Mohammadi and Salehi-Golsefidy gave necessary and sufficient conditions under
which certain translates of homogeneous measures converge, and they determined the …
which certain translates of homogeneous measures converge, and they determined the …
An avoidance principle and Margulis functions for expanding translates of unipotent orbits
A Sanchez, J Seong - arXiv preprint arXiv:2206.12019, 2022 - arxiv.org
We prove an avoidance principle for expanding translates of unipotent orbits for some
semisimple homogeneous spaces. In addition, we prove a quantitative isolation result of …
semisimple homogeneous spaces. In addition, we prove a quantitative isolation result of …
Expanding measures: Random walks and rigidity on homogeneous spaces
R Prohaska, C Sert, R Shi - Forum of Mathematics, Sigma, 2023 - cambridge.org
Let G be a real Lie group, a lattice and a connected semisimple subgroup without compact
factors and with finite center. We define the notion of H-expanding measures on H and …
factors and with finite center. We define the notion of H-expanding measures on H and …
Uniform distribution of orbits of lattices on spaces of frames
A Gorodnik - 2004 - projecteuclid.org
We study distribution of orbits of a lattice Γ⊆\SL(n,R) in the the space V_n,l of l-frames in
R^n (1≤l≤n-1). Examples of dense Γ-orbits are known from the work of Dani, Raghavan …
R^n (1≤l≤n-1). Examples of dense Γ-orbits are known from the work of Dani, Raghavan …
On the rate of equidistribution of expanding translates of horospheres in Γ/G.
SC Edwards - Commentarii Mathematici Helvetici, 2021 - ems.press
On the rate of equidistribution of expanding translates of horospheres in nG Page 1
Comment. Math. Helv. 96 (2021), 275–337 DOI 10.4171/CMH/513 Commentarii …
Comment. Math. Helv. 96 (2021), 275–337 DOI 10.4171/CMH/513 Commentarii …