Arithmeticity and topology of smooth actions of higher rank abelian groups

DOI10.3934/jmd.2016.10.135zbMath1370.37048arXiv1305.7262OpenAlexW2962741677MaRDI QIDQ316989

Federico Rodriguez Hertz, Anatole Katok

Publication date: 30 September 2016

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

Full work available at URL: https://arxiv.org/abs/1305.7262

zbMATH Keywords

entropyrigidityLyapunov exponentgeometric structureaction of higher rank abelian groupsarithmetic structure

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Finite transformation groups (57S17) 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 (7)

Normal forms for non-uniform contractions ⋮ On the work of Rodriguez Hertz on rigidity in dynamics ⋮ Lattice subgroups acting on manifolds ⋮ Anatole Katok ⋮ The Fried average entropy and slow entropy for actions of higher rank abelian groups ⋮ 𝑛-dimensional projective varieties with the action of an abelian group of rank 𝑛-1 ⋮ Flexibility of Lyapunov exponents

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global rigidity of higher rank abelian Anosov algebraic actions
• The Fried average entropy and slow entropy for actions of higher rank abelian groups
• Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups
• Nonuniform measure rigidity
• New criteria for ergodicity and nonuniform hyperbolicity
• On manifolds homeomorphic to the 7-sphere
• Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori
• Rigidity of real-analytic actions of \(SL(n,\mathbb Z)\) on \(\mathbb T^n\): a case of realization of Zimmer program
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems
• A result of Schinzel
• Synchronization of canonical measures for hyperbolic attractors
• Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus
• Global rigidity results for lattice actions on tori and new examples of volume-preserving actions
• Global rigidity of certain Abelian actions by toral automorphisms
• Uniqueness of large invariant measures for \(\mathbb Z^k\) actions with Cartan homotopy data
• Almost isometric actions, property (T), and local rigidity
• Groups of homotopy spheres. I
• Some ergodic properties of commuting diffeomorphisms
• A reduction of the Schoenflies extension problem
• Multi-Invariant Sets on Tori
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• Global rigidity of higher rank Anosov actions on tori and nilmanifolds
• On the product of the conjugates outside the unit circle of an algebraic number
• A proof of the generalized Schoenflies theorem
• On embeddings of spheres

This page was built for publication: Arithmeticity and topology of smooth actions of higher rank abelian groups