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 ∈ 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 codimension one Anosov endomorphism that is C¹-close to a linear endomorphism of ⁿ for (n ≥ 2).
@article{bwmeta1.element.bwnjournal-article-doi-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},
volume = {233},
year = {2016},
pages = {37-48},
zbl = {06622325},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm92-10-2015}
}
Fernando Micena; Ali Tahzibi. On the unstable directions and Lyapunov exponents of Anosov endomorphisms. Fundamenta Mathematicae, Tome 233 (2016) pp. 37-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm92-10-2015/