2024/10/21 by Carvalho, Bernardo · 1 citation
#Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2410.15740
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.