2018/04/16 by Lorenzo J. Díaz, Katrin Gelfert, Díaz, Lorenzo J. +3 · 1 citation
Mathematics · #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1804.05913
We study C1-robustly transitive and nonhyperbolic diffeomorphisms having a\npartially hyperbolic splitting with one-dimensional central bundle whose strong\nun-/stable foliations are both minimal. In dimension 3, an important class\nof examples of such systems is given by those with a simple closed periodic\ncurve tangent to the central bundle. We prove that there is a C1-open and\ndense subset of such diffeomorphisms such that every nonhyperbolic ergodic\nmeasure (i.e. with zero central exponent) can be approximated in the weak\∗\ntopology and in entropy by measures supported in basic sets with positive\n(negative) central Lyapunov exponent. Our method also allows to show how\nentropy changes across measures with central Lyapunov exponent close to zero.\nWe also prove that any nonhyperbolic ergodic measure is in the intersection of\nthe convex hulls of the measures with positive central exponent and with\nnegative central exponent.\n