Hyperbolic measures and commuting maps in low dimension | Zendy

Anatole Katok | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Hyperbolic measures and commuting maps in low dimension

Author(s) -

Anatole Katok

Publication year - 1996

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.1996.2.397

Subject(s) - lyapunov exponent , mathematics , measure (data warehouse) , dimension (graph theory) , pure mathematics , manifold (fluid mechanics) , invariant (physics) , hyperbolic set , degeneracy (biology) , action (physics) , mathematical analysis , mathematical physics , physics , nonlinear system , computer science , mechanical engineering , bioinformatics , quantum mechanics , database , engineering , biology

We study invariant measures with non{vanishing Lyapunov characterictic expo- nents for commuting dieomorphisms of compact manifolds. In particular we show that for k =2 ; 3n o faithfulZk real{analytic action on a k{dimensional manifold preserves a hyperbolic measure. In the smooth case similar statements hold for actions faithful on the support of the measure. Generalizations to higher dimension are proved under certain non{degeneracy condi- tions for the Lyapunov exponents.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research