Density of positive Lyapunov exponents for quasiperiodic SL(2, R)-cocycles in arbitrary dimension | Zendy

Artur Avila | Zendy

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Density of positive Lyapunov exponents for quasiperiodic <em>SL(2, R)</em>-cocycles in arbitrary dimension

Author(s) -

Artur Avila

Publication year - 2009

Publication title -

journal of modern dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.668

H-Index - 25

eISSN - 1930-532X

pISSN - 1930-5311

DOI - 10.3934/jmd.2009.3.631

Subject(s) - mathematics , lyapunov exponent , quasiperiodic function , rotation number , dimension (graph theory) , irrational number , zero (linguistics) , exponent , pure mathematics , mathematical analysis , mathematical physics , rotation (mathematics) , nonlinear system , quantum mechanics , geometry , physics , linguistics , philosophy

We show that given a fixed irrational rotation of the $d$-dimensional torus, any analytic SL(2, R)-cocycle can be perturbed in such a way that the Lyapunov exponent becomes positive. This result strengthens and generalizes previous results of Krikorian [6] and Fayad-Krikorian [5]. The key technique is the analyticity of $m$-functions (under the hypothesis of stability of zero Lyapunov exponents), first observed and used in the solution of the Ten-Martini Problem [2].

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