Dimension theory for multimodal maps

Details Dimension theory for multimodal maps Dimension theory for multimodal maps

2009-11-16

arxiv.org/abs/0911.3077v1

Annales Henri Poincar\'e 12, 591-620 (2011)

Mathematics

Dynamical Systems

Scientific paper

This paper is devoted to the study of dimension theory, in particular
multifractal analysis, for multimodal maps. We describe the Lyapunov spectrum,
generalising previous results by Todd. We also 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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