“…Furthermore, by using Katok's map, it is proved that every smooth compact manifold of dimension greater than two carries a hyperbolic diffeomorphism (see [4,5,11], and see also [15] for a flow version). Chen et al [9,10] and Hu et al [16] constructed systems that exhibit essential coexistence of chaotic and nonchaotic behaviors, where the chaotic parts are pointwise partially hyperbolic diffeomorphisms or pointwise hyperbolic flows. In the above examples, the systems are volume preserving.…”