Multifractal structure of a non-expanding dynamic defined on a Cantor set

The transformation of the interval studied, leaves invariant a Canter set o n which subsists a neutral fixed point. The non-expanding dynamical system defined is topologically conjugate to the full-shift on a two-symbol alphab et. We first prove that the ergodic measure are exact dimensional. Then, th e multifractal analysis of the g-measures is obtained by using the underlyi ng thermodynamic formalism. Finally, we prove an extension of the so-called Bowen formula which gives, the Hausdorff dimension of the Cantor set studi ed. (C) 2000 Academie des sciences/Editions scientifiques et medicales Else vier SAS.