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On the unstable directions and Lyapunov exponents of Anosov endomorphisms

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Micena F., Tahzibi A.

Fundamenta Mathematicae

2016

tom 235

nr 1

37-48

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).

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Micena F.

1 Tahzibi A.

1 2016

Wyniki wyszukiwania

On the unstable directions and Lyapunov exponents of Anosov endomorphisms