On the unstable directions and Lyapunov exponents of Anosov endomorphisms

• Autorzy: Fernando Micena , Ali Tahzibi
• Języki publikacji: EN

Abstrakty

EN

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 𝕋ⁿ for (n ≥ 2).

Kategorie tematyczne

• 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 235
• Numer: 1
• Strony: 37-48

Daty

wydano

2016

Twórcy

autor

Fernando Micena

• Departamento de Matemática, IM-UFAL, Maceió, AL, Brazil

autor

Ali Tahzibi

• Departamento de Matemática, ICMC-USP, São Carlos, SP, Brazil

Identyfikatory

DOI

10.4064/fm92-10-2015