Rigidity of measures -- the high entropy case and non-commuting foliations

DOI10.1007/BF02775436zbMath1097.37017OpenAlexW2098449382MaRDI QIDQ814153

Anatole Katok, Manfred Einsiedler

Publication date: 6 February 2006

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02775436

zbMATH Keywords

entropyinvariant measuresrigidityinvariant foliationshyperbolic actions

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (19)

Joinings of higher-rank diagonalizable actions on locally homogeneous spaces ⋮ On the work of Rodriguez Hertz on rigidity in dynamics ⋮ Divisibility properties of higher rank lattices ⋮ C¹ actions on manifolds by lattices in Lie groups ⋮ Diagonal actions in positive characteristic ⋮ Joinings of higher rank torus actions on homogeneous spaces ⋮ Simultaneous dense and nondense orbits for commuting maps ⋮ Lattice subgroups acting on manifolds ⋮ Smooth ergodic theory of \(\mathbb{Z}^d \)-actions ⋮ Diophantine approximations on fractals ⋮ Symmetry of entropy in higher rank diagonalizable actions and measure classification ⋮ Anatole Katok ⋮ Commuting foliations ⋮ Distribution of periodic torus orbits on homogeneous spaces ⋮ The work of Einsiedler, Katok and Lindenstrauss on the Littlewood conjecture ⋮ Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds ⋮ On \(C^*\)-algebras of irreversible algebraic dynamical systems ⋮ On measures invariant under tori on quotients of semisimple groups ⋮ Rigidity properties for commuting automorphisms on tori and solenoids

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