On the Classification of Resonance-free Anosov Z Actions
نویسندگان
چکیده
We consider actions of Z, k ≥ 2, by Anosov diffeomorphisms which are uniformly quasiconformal on each coarse Lyapunov distribution. These actions generalize Cartan actions for which coarse Lyapunov distributions are onedimensional. We show that, under certain non-resonance assumptions on the Lyapunov exponents, a finite cover of such an action is smoothly conjugate to an action by toral automorphisms.
منابع مشابه
On Classification of Resonance-free Anosov Z Actions
We consider actions of Z, k ≥ 2, by Anosov diffeomorphisms which are uniformly quasiconformal on each coarse Lyapunov distribution. These actions generalize Cartan actions for which coarse Lyapunov distributions are onedimensional. We show that, under certain non-resonance assumptions on the Lyapunov exponents, a finite cover of such an action is smoothly conjugate to an action by toral automor...
متن کاملThe Katok-spatzier Conjecture and Generalized Symmetries
Within the smooth category, an intertwining is exhibited between the global rigidity of irreducible higher-rank Z Anosov actions on T and the classification of equilibrium-free flows on T that possess nontrivial generalized symmetries.
متن کاملSpatzier’s Conjecture and Generalized Symmetries
Within the smooth category, an intertwining is exhibited between the global rigidity of irreducible higher-rank Z Anosov actions on T and the classification of equilibrium-free flows on T that possess nontrivial generalized symmetries.
متن کاملGlobal Rigidity of Higher Rank Anosov Actions on Tori and Nilmanifolds
An Anosov diffeomorphism f on a torus T is affine if f lifts to an affine map on R. By a classical result of Franks and Manning, any Anosov diffeomorphism g on T is topologically conjugate to an affine Anosov diffeomorphism. More precisely, there is a homeomorphism φ : T → T such that f = φ◦g◦φ−1 is an affine Anosov diffeomorphism. We call φ the Franks-Manning conjugacy. The linear part of f is...
متن کاملLocal rigidity of certain partially hyperbolic actions of product type
We prove certain rigidity properties of higher-rank abelian product actions of the type α × Id N : Z κ → Diff(M × N), where α is (TNS) (i.e. is hyperbolic and has some special structure of its stable distributions). Together with a result about product actions of property (T) groups, this implies the local rigidity of higher-rank lattice actions of the form α × Id T : → Diff(M × T), provided α ...
متن کامل