Thermodynamic Formalism and Multifractal Analysis of Conformal Infinite Iterated211 Function Systems

摘要

In this paper the authors develop the thermodynamic formalism for equilibrium211u001estates of strongly Holder families of functions. These equilibrium states are 211u001esupported on the limit set generated by iterating a system of infinitely many 211u001econtractions. The first five sections of this paper except Section 3 are devoted 211u001eto developing the thermodynamic formalism for equilibrium states of Holder 211u001efamilies of functions. The first two sections contain material part of which can 211u001ealso be found in (HU) and (Ur). These sections along with Section 3 provide the 211u001eauthors with the tools needed to carry out the multifractal analysis for the 211u001eequilibrium states mentioned above assuming that the limit set is generated by 211u001econformal contractions. The theory of infinite systems of conformal contractions 211u001eis laid out in (MU1). The multifractal analysis is then given in Section 7. In 211u001eSection 8 the authors apply this theory to some examples from continued fraction 211u001esystems and Apollonian packing.