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arXiv · 2410.15740

Transitivity of real Anosov diffeomorphisms

Bernardo Carvalho
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Abstract

We prove the transitivity of real Anosov diffeomorphisms, which are Anosov diffeomorphisms where stable and unstable spaces decompose into a continuous sum of invariant one-dimensional sub-spaces with uniform contraction/expansion over the ambient manifold. We prove that if a stable/unstable curve has a well-defined length in a conformal hyperbolic distance, then it has a globally defined holonomy. We exhibit a conformal hyperbolic distance with well-defined length of stable/unstable curves for each real Anosov diffeomorphism.

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Bernardo Carvalho. 2024-10-21. Transitivity of real Anosov diffeomorphisms. https://arxiv.org/abs/2410.15740

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