2014/12/01 by Fernando Micena, Micena, F., Ali Tahzibi +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Topology and Set Theory #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1412.0629
openalex publication_date 2014/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Despite the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under transitivity assumption, that an Anosov endomorphism on 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. Other result of this work is the semi rigidity of the unstable Lyapunov exponent of a C1+α codimension one Anosov endomorphism and C1 close to a linear endomorphism of \mathbbTn for (n ≥ 2). In the appendix we give a proof for ergodicity of C1+α, α> 0, conservative Anosov endomorphism.