Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori

zbMath1173.37017arXivmath/0602176MaRDI QIDQ875727

Anatole Katok, Boris Kalinin

Publication date: 13 April 2007

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602176

zbMATH Keywords

nonuniform hyperbolicitymeasure rigidity\(Z^k\) actions

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) 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 (14)

Measure rigidity for random dynamics on surfaces and related skew products ⋮ Normal forms for non-uniform contractions ⋮ Arithmeticity and topology of smooth actions of higher rank abelian groups ⋮ Global smooth and topological rigidity of hyperbolic lattice actions ⋮ Lattice subgroups acting on manifolds ⋮ Totally nonsymplectic Anosov actions on tori and nilmanifolds ⋮ Open sets of partially hyperbolic skew products having a unique SRB measure ⋮ Smooth ergodic theory of \(\mathbb{Z}^d \)-actions ⋮ Nonuniform measure rigidity ⋮ Anatole Katok ⋮ Smooth stabilizers for measures on the torus ⋮ Non-uniform measure rigidity for ℤ^{𝕜} actions of symplectic type ⋮ Global rigidity of higher rank Anosov actions on tori and nilmanifolds ⋮ Smooth mixing Anosov flows in dimension three are exponentially mixing

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