Stationary measures and closed invariants on homogeneous spaces

DOI10.4007/annals.2011.174.2.8zbMath1241.22007OpenAlexW2090614326WikidataQ56005107 ScholiaQ56005107MaRDI QIDQ640808

Yves Benoist, Jean-François Quint

Publication date: 20 October 2011

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4007/annals.2011.174.2.8

zbMATH Keywords

Lie groupshomogeneous spacestationary measurehorocyclic flowsclosed invariantsHaar probability

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) General properties and structure of real Lie groups (22E15) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items

Measure rigidity for random dynamics on surfaces and related skew products, Central limit theorem for linear groups, Linear random walks on the torus, Spectral gap properties for linear random walks and Pareto's asymptotics for affine stochastic recursions, Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space, Multi-invariant measures and subsets on nilmanifolds, Random walks with bounded first moment on finite-volume spaces, Stationary measures and invariant subsets of homogeneous spaces. III., Semisimplicity of the Lyapunov spectrum for irreducible cocycles, Hausdorff dimension of limit sets, Random walks on homogeneous spaces and Diophantine approximation on fractals, Radon stationary measures for a random walk on \(\mathbb{T}^d\times\mathbb{R}\), On Bohr sets of integer-valued traceless matrices, Expanding measures: Random walks and rigidity on homogeneous spaces, Noncommutative ergodic theory of higher rank lattices, Finitary analysis in homogeneous spaces, Random dynamics on real and complex projective surfaces, Open sets of partially hyperbolic skew products having a unique SRB measure, Some asymptotic properties of random walks on homogeneous spaces, Random walks, spectral gaps, and Khintchine's theorem on fractals, A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces, Measure rigidity of Anosov flows via the factorization method, Projections of Patterson-Sullivan measures and the dichotomy of Mohammadi-Oh, Generic stationary measures and actions, Markov random walks on homogeneous spaces and Diophantine approximation on fractals, Random walks on random coset spaces with applications to Furstenberg entropy, Extreme value theory for random walks on homogeneous spaces, Spread out random walks on homogeneous spaces, Dynamics on the space of 2-lattices in 3-space, Joining measures for horocycle flows on abelian covers, Characteristic polynomial patterns in difference sets of matrices, Topological proof of Benoist-Quint's orbit closure theorem for \(\mathrm{SO}(d, 1) \), Discretized sum-product estimates in matrix algebras, Recurrence on affine Grassmannians, Random matrix products when the top Lyapunov exponent is simple, Equidistribution in \(S\)-arithmetic and adelic spaces, Invariant Radon measures for Unipotent flows and products of Kleinian groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Raghunathan's topological conjecture and distributions of unipotent flows
• Invariant measures and the set of exceptions to Littlewood's conjecture
• Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits
• Invariant measures and stiffness for non-Abelian groups of toral automorphisms
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• On Raghunathan's measure conjecture
• Invariant measures for actions of unipotent groups over local fields on homogeneous spaces
• Semigroup action on \(\mathbb T^n\)
• Convergence of spherical averages for actions of free groups
• Unipotent flows and counting lattice points on homogeneous varieties
• Frontière de furstenberg, propriétés de contraction et théorèmes de convergence
• A proof of the estimation from below in Pesin's entropy formula
• Ergodic theoretic proof of equidistribution of Hecke points
• Actions of large semigroups and random walks on isometric extensions of boundaries
• Countable sections for locally compact group actions
• [https://portal.mardi4nfdi.de/wiki/Publication:4094203 K-flots et th�or�me de renouvellement]
• Orbits of linear group actions, random walks on homogeneous spaces and toral automorphisms
• Invariant measures for higher-rank hyperbolic abelian actions
• Products of Random Matrices
• LECTURES ON THE ENTROPY THEORY OF MEASURE-PRESERVING TRANSFORMATIONS
• Noncommuting Random Products
• A general ergodic theorem
• Hecke operators and equidistribution of Hecke points