Abstract
We calculate the value of teh average of the singularities of a Gibbs measure μ invariant with respect to an expansiveC 2 diffeomorphism of a one-compact manifold. This is the value related to dimension that one computes numerically. We then define and study a function, known as the correlation dimension, which is related to a free energy function, and we generalize the results in higher dimension with an axiomA transformation acting on a two-compact manifold.
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Communicated by J.-P. Eckmann
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Simpelaere, D. Mean of the singularities of a Gibbs measure. Commun.Math. Phys. 179, 489–510 (1996). https://doi.org/10.1007/BF02102598
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DOI: https://doi.org/10.1007/BF02102598