Symbolic dynamics for certain non-invertible $C^{1+{\hat{I}}^2}$ maps

Jing Xun, Yifan Zhang, Yujun Zhu

Let $f$ be a non-invertible $C^{1+{\hat{I}}^2}({\hat{I}}^2>0)$ map with zero Lyapunov exponents and singularities on a closed Riemannian manifold $M$. We consider the symbolic dynamics of $f$. Combi…