THERMODYNAMIQUE　DES　ENSEMBLES　DE　CANTOR　AUTOSIMILAIRES　（THERMODYNAMICS　OF　SELF－SIMILAR　CANTOR　SETS）  

作　　者：G. MICHON  J. PEYRIERE(University de Bourgogne, URA 755, BP 138, 21004 Dijon, dance.)(University de Paris-Sud, Centre d’Orsayl URA 757, 91405 Orsayt dance.) 

出　　处：《Chinese Annals of Mathematics,Series B》1994年第3期253-272,共20页数学年刊（B辑英文版）

摘　　要：A class of metric, compact, and totally disconllected spaces, called self-similar Cantor setsis illtroduced. A self-similar structure is defined to be a graph with weighted edges. Theintroduction of ultrametrics and quasi-isometries gives versatility to this construction. Thermodynamical functions as free energy and elltropy are associated with self-similar structures.Multifractal analysis, based on a 'Large Deviations' inequality and Gibbs measures, leads toa fairly general Hausdoffi dimension theorem.

关 键 词：Cantor set Graph Dimension THERMODYNAMICS Gibbs meajsure Multifractals. 

分 类 号：O174.12[理学—数学] O157.5[理学—基础数学]