Hausdorff dimensions of recurrent and shrinking target sets under Lipschitz functions for expanding Markov maps

Abstract

Let T be an expanding Markov map with a repeller E defined on . This paper concerns the Hausdorff dimension of the sets and where is a sequence of Lipschitz functions with a uniform Lipschitz constant, , f is a positive continuous function on , is the sum and ψ is a positive function defined on . The results can be applied to cookie-cutter dynamical systems and continued fraction dynamical systems, etc.