Dimension spectrum of asymptotically additive potentials for C1 average conformal repellers

In this paper, the dimension spectrum of asymptotically additive potentials for C1 average conformal repellers is considered. First, we give dimension estimates of arbitrary subsets for C1 average conformal repellers and we also consider the pointwise dimension of invariant measures. Furthermore, we consider the dimension spectrum of asymptotically additive potentials and its properties. As applications, we give an affirmative answer to the problem posed by Olsen (2003 J. Math. Pures Appl. 82 1591–649) for general types of level sets and obtain the dimension spectrum of weak Gibbs measures for continuous potentials on C1 average conformal repellers. (paper)