Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
Annals of mathematics, Tome 167 (2008) no. 2, pp. 643-680
We prove that for any $s>0$ the majority of $C^s$ linear cocycles over any hyperbolic (uniformly or not) ergodic transformation exhibit some nonzero Lyapunov exponent: this is true for an open dense subset of cocycles and, actually, vanishing Lyapunov exponents correspond to codimension-$\infty$. This open dense subset is described in terms of a geometric condition involving the behavior of the cocycle over certain heteroclinic orbits of the transformation.
@article{10_4007_annals_2008_167_643,
author = {Marcelo Viana},
title = {Almost all cocycles over any hyperbolic system have nonvanishing {Lyapunov} exponents},
journal = {Annals of mathematics},
pages = {643--680},
year = {2008},
volume = {167},
number = {2},
doi = {10.4007/annals.2008.167.643},
mrnumber = {2415384},
zbl = {1173.37019},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2008.167.643/}
}
TY - JOUR AU - Marcelo Viana TI - Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents JO - Annals of mathematics PY - 2008 SP - 643 EP - 680 VL - 167 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2008.167.643/ DO - 10.4007/annals.2008.167.643 LA - en ID - 10_4007_annals_2008_167_643 ER -
%0 Journal Article %A Marcelo Viana %T Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents %J Annals of mathematics %D 2008 %P 643-680 %V 167 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2008.167.643/ %R 10.4007/annals.2008.167.643 %G en %F 10_4007_annals_2008_167_643
Marcelo Viana. Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. Annals of mathematics, Tome 167 (2008) no. 2, pp. 643-680. doi: 10.4007/annals.2008.167.643
Cité par Sources :