Partially hyperbolic sets with positive
measure and $ACIP$ for partially hyperbolic systems
Pengfei Zhang  School of Mathematical Sciences, Peking University, Beijing 100871, China (email) Abstract:
In [23] Xia introduced a simple dynamical density basis for
partially hyperbolic sets of volume preserving diffeomorphisms. We
apply the density basis to the study of the topological structure of
partially hyperbolic sets. We show that if $\Lambda$ is a strongly
partially hyperbolic set with positive volume, then $\Lambda$
contains the global stable manifolds over ${\alpha}(\Lambda^d)$ and
the global unstable manifolds over ${\omega}(\Lambda^d)$.
Keywords: Partially hyperbolic, positive volume, dynamical density
basis, $acip$ measure, weak ergodicity, transitive, accessible, saturated.
Received: June 2010; Revised: August 2011; Available Online: October 2011. 
2016 Impact Factor1.099
