Ergodic Measures with Multi-zero Lyapunov Exponents Inside Homoclinic Classes

Abstract

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.