Abstract
This paper is devoted to the study of dimension theory, in particular multifractal analysis, for multimodal maps. We describe the Lyapunov spectrum and study the multifractal spectrum of pointwise dimension. The lack of regularity of the thermodynamic formalism for this class of maps is reflected in the phase transitions of the spectra.
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Communicated by Viviane Baladi.
GI was partially supported by Proyecto Fondecyt 11070050. MT was partially supported by FCT grant SFRH/BPD/26521/2006 and also by FCT through CMUP.
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Iommi, G., Todd, M. Dimension Theory for Multimodal Maps. Ann. Henri Poincaré 12, 591–620 (2011). https://doi.org/10.1007/s00023-011-0086-3
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DOI: https://doi.org/10.1007/s00023-011-0086-3