2017/07/13 by Gogolev, Andrey, Maimon, Itai, Kolmogorov, Aleksey N.
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1707.04303
We consider a hyperbolic automorphism A\colon\mathbb T3→\mathbb T3 of the 3-torus whose 2-dimensional unstable distribution splits into weak and strong unstable subbundles. We unfold A into two one-parameter families of Anosov diffeomorphisms --- a conservative family and a dissipative one. For diffeomorphisms in these families we numerically calculate the strong unstable manifold of the fixed point. Our calculations strongly suggest that the strong unstable manifold is dense in \mathbb T3. Further, we calculate push-forwards of the Lebesgue measure on a local strong unstable manifold. These numeric data indicate that the sequence of push-forwards converges to the SRB measure.