Regularity and convergence rates for the Lyapunov exponents of linear cocycles | Zendy

Wilhelm Schlag | Zendy

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Regularity and convergence rates for the Lyapunov exponents of linear cocycles

Author(s) -

Wilhelm Schlag

Publication year - 2013

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.2013.7.619

Subject(s) - mathematics , lyapunov exponent , diophantine equation , diophantine approximation , omega , torus , combinatorics , rate of convergence , ball (mathematics) , compact space , discrete mathematics , mathematical analysis , geometry , physics , key (lock) , quantum mechanics , nonlinear system , biology , ecology

We study linear co-cycles in GL(d,R) (or C) depending on a parameter (in a Lipschitz or Holder fashion) and establish Holder regularity of the Lyapunov exponents for the shift dynamics on the base. We also obtain rates of convergence of the finite volume exponents to their infinite volume limits. The technique is that developed jointly with Michael Goldstein for Schroedinger co-cycles. In particular, we extend the Avalanche Principle, which had been formulated originally for SL(2,R) co-cycles, to GL(d,R).

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