Abstract This is the first paper in a two-part series containing some results on dimension estimates for $C^1$ iterated function systems and repellers. In this part, we prove that upper box-counting of attractor any system (IFS) ${\Bbb R}^d$ bounded above by its singularity dimension, packing ergodic invariant measure associated with IFS Lyapunov dimension. Similar are obtained repellers expand...

Abstract This is the second part of our study on dimension theory $C^1$ iterated function systems (IFSs) and repellers $\mathbb {R}^d$ . In first [D.-J. Feng K. Simon. Dimension estimates for repellers. Part I. Preprint , 2020, arXiv:2007.15320], we proved that upper box-counting attractor every IFS ${\Bbb R}^d$ bounded above by its singularity dimension, packing ergodic invariant measure assoc...