Dimension theory for multimodal maps

Abstract

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.

References in corpus (3)

• Equilibrium states for potentials with $\supϕ- \infϕ< \htop(f)$
• Natural equilibrium states for multimodal maps
• The Lyapunov spectrum is not always concave

Cited by in corpus (6)

• The thermodynamic approach to multifractal analysis
• Large deviation principle for Benedicks-Carleson quadratic maps
• Multifractal formalism for Benedicks-Carleson quadratic maps
• Slow and fast escape for open intermittent maps
• Lyapunov spectrum for multimodal maps
• Multifractal analysis in non-uniformly hyperbolic interval maps