中文摘要：

对于给定紧光滑黎曼流形M上的一个C^2保体积部分双曲微分同胚f,若对所有不变测度的中心方向的指数都满足中心指数约束条件,则f本质可达蕴含遍历.特别地,若对所有不变测度,中心方向指数都为零,则f本质可达蕴含遍历.这一结果部分回答了Pesin提出的两个公开问题.

英文摘要：

Let M be a smooth compact Riemmannian manifold, f be a C^2 partially hyperbolic diffeomorphism preserving volume. If f is essential accessible and the central exponents satisfy center bunching condition for all invariant measure, then f is ergodic. Especially, if for all invariant measure of f, the central exponents are zero, then essential accessibility implies ergodicity. These results partially answer two open problems.