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| THERMODYNAMIQUE DESENSEMBLES DE CANTORAUTOSIMILAIRES |
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Citation： |
G. Michon,J. Peyri.THERMODYNAMIQUE DESENSEMBLES DE CANTORAUTOSIMILAIRES[J].Chinese Annals of Mathematics B,1994,15(3):253~272 |
| Page view： 817
Net amount： 585 |
Authors： |
G. Michon; J. Peyri |
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| Abstract： |
A class of metric, compact, and totally
disconnected spaces, called self-similar Cantor sets is introduced. A
self-similar structure is defined to be a graph with weighted edges.
The introduction
of ultrametrics and quasi-isometries gives versatility to this
construction. Thermodynamical functions as free energy and entropy are
associated with self-similar structures. Multifractal analysis, based on
a ``Large Deviations'' inequality and Gibbs measures, leads to a
fairly general Hausdorff dimension theorem. |
Keywords： |
Cantor set, Graph, Dimension, Thermodynamics,
Gibbs measure,Multifractals. |
Classification： |
54F65, 54F45, 05C50, 82A05. |
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