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

Jing Xun, Yifan Zhang, Yujun Zhu

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