Local rigidity of Lyapunov spectrum for toral automorphisms

DOI10.1007/s11856-020-2028-6zbMath1452.37022arXiv1808.06249OpenAlexW3033560842MaRDI QIDQ2200041

Victoria Sadovskaya, Boris Kalinin, Andrey Gogolev

Publication date: 15 September 2020

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

Full work available at URL: https://arxiv.org/abs/1808.06249

zbMATH Keywords

Lyapunov exponentsAnosov automorphismsmall perturbationpartially hyperbolic automorphisms

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (9)

Anosov endomorphisms on the two-torus: regularity of foliations and rigidity ⋮ Smooth local rigidity for hyperbolic toral automorphisms ⋮ Rigidity of stable Lyapunov exponents and integrability for Anosov maps ⋮ Joint integrability and spectral rigidity for Anosov diffeomorphisms ⋮ Local rigidity of certain solvable group actions on tori ⋮ Local Lyapunov spectrum rigidity of nilmanifold automorphisms ⋮ Local rigidity for hyperbolic toral automorphisms ⋮ Flexibility of Lyapunov exponents ⋮ Carnot metrics, dynamics and local rigidity

Cites Work

• Unnamed Item
• Unnamed Item
• Representations of toral automorphisms
• Cocycles with one exponent over partially hyperbolic systems
• Linear cocycles over hyperbolic systems and criteria of conformality
• Livšic theorem for matrix cocycles
• Stable ergodicity of certain linear automorphisms of the torus
• A regularity lemma for functions of several variables
• C\({}^ k\)-rigidity for hyperbolic flows. II
• Extremal Lyapunov exponents: an invariance principle and applications
• Smooth conjugacy of anosov diffeomorphisms on higher-dimensional tori
• Invariants for smooth conjugacy of hyperbolic dynamical systems. II
• Invariants for smooth conjugacy of hyperbolic dynamical systems. IV
• Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems
• Lectures on partial hyperbolicity and stable ergodicity
• Cohomology of \(\mathrm{GL}(2,\mathbb{R})\)-valued cocycles over hyperbolic systems
• Propriétés ergodiques des mesures de Sinaï
• Lyapunov exponents and rigidity of Anosov automorphisms and skew products
• Local rigidity for Anosov automorphisms. With an appendix by Rafael de la Llave
• Homology properties of Y-systems
• Livsic theorems for connected Lie groups
• A proof of the estimation from below in Pesin's entropy formula
• On Anosov diffeomorphisms with asymptotically conformal periodic data
• ON LOCAL AND GLOBAL RIGIDITY OF QUASI-CONFORMAL ANOSOV DIFFEOMORPHISMS
• Rigidity of higher-dimensional conformal Anosov systems
• Further rigidity properties of conformal Anosov systems
• Cohomology of fiber bunched cocycles over hyperbolic systems
• Invariant manifolds

This page was built for publication: Local rigidity of Lyapunov spectrum for toral automorphisms