On Arnol’d’s and Kazhdan’s equidistribution problems

DOI10.1017/S0143385711000721zbMath1261.37006arXiv1009.5076OpenAlexW2963240784MaRDI QIDQ4911054

Alexander Gorodnik, Amos Nevo

Publication date: 13 March 2013

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.5076

zbMATH Keywords

homogeneous spacesmean ergodic theoremequidistribution problemsratio ergodic theoremisometric actions of lattices

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items

Ergodic theory and the duality principle on homogeneous spaces ⋮ Quantitative ergodic theorems and their number-theoretic applications ⋮ Aperiodic order and spherical diffraction. II: Translation bounded measures on homogeneous spaces

Cites Work

• Unnamed Item
• Unnamed Item
• On mixing properties of compact group extensions of hyperbolic systems
• Uniform distribution of orbits of lattices on spaces of frames
• The Ruziewicz problem and distributing points on homogeneous spaces of a compact Lie group
• Distribution of lattice orbits on homogeneous varieties
• Spectral transfer and pointwise ergodic theorems for semi-simple Kazhdan groups
• Analogs of Wiener's ergodic theorems for semisimple Lie groups. II
• Automorphic forms and the distribution of points on odd-dimensional spheres.
• Orbit distribution on \(\mathbb R^2\) under the natural action of \(\mathrm{SL}(2,\mathbb Z)\)
• Ergodic properties of linear actions of \((2\times 2)\)-matrices
• Orbits of discrete subgroups on a symmetric space and the Furstenberg boundary
• On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\)
• Proximality and equidistribution on the Furstenberg boundary
• Distribution results for lattices in \(\text{SL}(2,\mathbb Q_p)\)
• The Ergodic Theory of Lattice Subgroups (AM-172)
• Hecke operators and distributing points on the sphere I
• Hecke operators and distributing points on S². II
• Distribution des orbites des réseaux sur le plan réel
• Lattice action on the boundary of SL $(n,\mathbb{R})}$
• Equidistribution of dense subgroups on nilpotent Lie groups