On the unstable directions and Lyapunov exponents of Anosov endomorphisms
Fundamenta Mathematicae, Tome 235 (2016) no. 1, pp. 37-48
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Unlike in the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under the transitivity assumption, that an Anosov endomorphism of a closed manifold $M$ is either special (that is, every $x \in M$ has only one unstable direction), or for a typical point in $M$ there are infinitely many unstable directions. Another result is the semi-rigidity of the unstable Lyapunov exponent of a $C^{1+\alpha }$ codimension one Anosov endomorphism that is $C^1$-close to a linear endomorphism of $\mathbb {T}^n$ for $(n \geq 2).$
Keywords:
unlike invertible setting anosov endomorphisms may have infinitely many unstable directions here prove under transitivity assumption anosov endomorphism closed manifold either special every has only unstable direction typical point there infinitely many unstable directions another result semi rigidity unstable lyapunov exponent alpha codimension anosov endomorphism close linear endomorphism mathbb geq
Affiliations des auteurs :
Fernando Micena 1 ; Ali Tahzibi 2
@article{10_4064_fm92_10_2015,
author = {Fernando Micena and Ali Tahzibi},
title = {On the unstable directions and {Lyapunov} exponents of {Anosov} endomorphisms},
journal = {Fundamenta Mathematicae},
pages = {37--48},
publisher = {mathdoc},
volume = {235},
number = {1},
year = {2016},
doi = {10.4064/fm92-10-2015},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm92-10-2015/}
}
TY - JOUR AU - Fernando Micena AU - Ali Tahzibi TI - On the unstable directions and Lyapunov exponents of Anosov endomorphisms JO - Fundamenta Mathematicae PY - 2016 SP - 37 EP - 48 VL - 235 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/fm92-10-2015/ DO - 10.4064/fm92-10-2015 LA - en ID - 10_4064_fm92_10_2015 ER -
%0 Journal Article %A Fernando Micena %A Ali Tahzibi %T On the unstable directions and Lyapunov exponents of Anosov endomorphisms %J Fundamenta Mathematicae %D 2016 %P 37-48 %V 235 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/fm92-10-2015/ %R 10.4064/fm92-10-2015 %G en %F 10_4064_fm92_10_2015
Fernando Micena; Ali Tahzibi. On the unstable directions and Lyapunov exponents of Anosov endomorphisms. Fundamenta Mathematicae, Tome 235 (2016) no. 1, pp. 37-48. doi: 10.4064/fm92-10-2015
Cité par Sources :