75 research outputs found
Genericity of zero Lyapunov exponents
We show that, for any compact surface, there is a residual (dense )
set of area preserving diffeomorphisms which either are Anosov or have
zero Lyapunov exponents a.e. This result was announced by R. Mane, but no proof
was available. We also show that for any fixed ergodic dynamical system over a
compact space, there is a residual set of continuous -cocycles which
either are uniformly hyperbolic or have zero exponents a.e.Comment: 28 pages, 1 figure. This is a revised, more readable, version of the
preprint distributed in 200
Generic linear cocycles over a minimal base
We prove that a generic linear cocycle over a minimal base dynamics of finite
dimension has the property that the Oseledets splitting with respect to any
invariant probability coincides almost everywhere with the finest dominated
splitting. Therefore the restriction of the generic cocycle to a subbundle of
the finest dominated splitting is uniformly subexponentially quasiconformal.
This extends a previous result for SL(2,R)-cocycles due to Avila and the
author.Comment: 17 pages, 1 figur
Perturbation of the Lyapunov spectra of periodic orbits
We describe all Lyapunov spectra that can be obtained by perturbing the
derivatives along periodic orbits of a diffeomorphism. The description is
expressed in terms of the finest dominated splitting and Lyapunov exponents
that appear in the limit of a sequence of periodic orbits, and involves the
majorization partial order. Among the applications, we give a simple criterion
for the occurrence of universal dynamics.Comment: A few improvements were made, based on the referee's suggestion
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