Geodesic
On the unstable directions and Lyapunov exponents of Anosov endomorphisms
Fernando Micena 1   ; Ali Tahzibi 2
1 Departamento de Matemática IM-UFAL Maceió, AL, Brazil
2 Departamento de Matemática ICMC-USP São Carlos, SP, Brazil
Fundamenta Mathematicae, Tome 235 (2016) no. 1, pp. 37-48 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $(n \geq 2).$
DOI : 10.4064/fm92-10-2015
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

Fernando Micena  1   ; Ali Tahzibi  2

1 Departamento de Matemática IM-UFAL Maceió, AL, Brazil
2 Departamento de Matemática ICMC-USP São Carlos, SP, Brazil 
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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

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