On the unstable directions and Lyapunov exponents of Anosov endomorphisms

Fernando Micena, and Ali Tahzibi. "On the unstable directions and Lyapunov exponents of Anosov endomorphisms." Fundamenta Mathematicae 235.1 (2016): 37-48. <http://eudml.org/doc/286115>.

@article{FernandoMicena2016,
abstract = {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 $C^\{1+α\}$ codimension one Anosov endomorphism that is C¹-close to a linear endomorphism of ⁿ for (n ≥ 2).},
author = {Fernando Micena, Ali Tahzibi},
journal = {Fundamenta Mathematicae},
keywords = {Anosov endomorphisms; unstable directions; Lyapunov exponents},
language = {eng},
number = {1},
pages = {37-48},
title = {On the unstable directions and Lyapunov exponents of Anosov endomorphisms},
url = {http://eudml.org/doc/286115},
volume = {235},
year = {2016},
}

TY - JOUR
AU - Fernando Micena
AU - Ali Tahzibi
TI - On the unstable directions and Lyapunov exponents of Anosov endomorphisms
JO - Fundamenta Mathematicae
PY - 2016
VL - 235
IS - 1
SP - 37
EP - 48
AB - 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 $C^{1+α}$ codimension one Anosov endomorphism that is C¹-close to a linear endomorphism of ⁿ for (n ≥ 2).
LA - eng
KW - Anosov endomorphisms; unstable directions; Lyapunov exponents
UR - http://eudml.org/doc/286115
ER -