DIMENSION ESTIMATES FOR ARBITRARY SUBSETS OF LIMIT SETS OF A MARKOV CONSTRUCTION AND RELATED MULTIFRACTAL ANALYSIS

摘要

Without constructing any measure and using properties of Markov partition, this paper provides a direct proof of dimension estimates for any subset of a limit set of a Markov construction. Furthermore, this paper investigate the dimensions of asymptotically conformal repellers. And the dimension spectrum of the level sets of nonadditive potentials on asymptotically conformal repellers are also obtained.