In this paper, we prove that for \(C^1\)-generic diffeomorphisms, if a homoclinic class contains periodic orbits of indices i and j with \(j>i+1\), and the homoclinic class has no-domination of index l for any \(l\in \{i+1,\ldots ,j-1\}\), then there exists a non-hyperbolic ergodic measure with more than one vanishing Lyapunov exponents and whose support is the whole homoclinic class. Some other results are also obtained.

中文翻译：

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同质类中具有多个零Lyapunov指数的遍历测度

在本文中，我们证明了对于\（C ^ 1 \）泛亚同构，如果同宿类包含索引为i和j且具有\（j> i + 1 \）的周期轨道，并且同宿类具有非支配性对于任何\（l \ in \ {i + 1，\ ldots，j-1 \} \）的索引l，则存在一个非双曲遍历测度，具有多个消失的Lyapunov指数，并且其支持是整个同宿点类。还可以获得其他一些结果。