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 q...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.展开更多
文摘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.
