General multifractal analysis of local entropies
Fundamenta Mathematicae, Tome 165 (2000) no. 3, pp. 203-237
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We address the problem of the multifractal analysis of local entropies for arbitrary invariant measures. We obtain an upper estimate on the multifractal spectrum of local entropies, which is similar to the estimate for local dimensions. We show that in the case of Gibbs measures the above estimate becomes an exact equality. In this case the multifractal spectrum of local entropies is a smooth concave function. We discuss possible singularities in the multifractal spectrum and their relation to phase transitions.
@article{10_4064_fm_165_3_203_237,
author = {Floris Takens and Evgeny Verbitski},
title = {General multifractal analysis of local entropies},
journal = {Fundamenta Mathematicae},
pages = {203--237},
publisher = {mathdoc},
volume = {165},
number = {3},
year = {2000},
doi = {10.4064/fm-165-3-203-237},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-165-3-203-237/}
}
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Floris Takens; Evgeny Verbitski. General multifractal analysis of local entropies. Fundamenta Mathematicae, Tome 165 (2000) no. 3, pp. 203-237. doi: 10.4064/fm-165-3-203-237
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