Ergodic Measures with Multi-zero Lyapunov Exponents Inside Homoclinic Classes

摘要

In this paper, we prove that for C-1-generic diffeomorphisms, if a homoclinic class contains periodic orbits of indices i and j with ji+1, and the homoclinic class has no-domination of index l for any l is an element of{i+1, horizontal ellipsis ,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.