Lyapunov spectrum for multimodal maps

TL;DR

This paper investigates the spectrum of Lyapunov exponents in multimodal interval maps and rational maps, providing insights into their dimension properties and dynamical complexity.

Contribution

It introduces new results on the Lyapunov spectrum for multimodal maps and extends the analysis to rational maps on the Riemann sphere.

Findings

Dimension spectrum characterized for multimodal maps

Results extended to rational maps on the Riemann sphere

Insights into dynamical complexity of these maps

Abstract

We study the dimension spectrum of Lyapunov exponents for multimodal maps of the interval and their generalizations. We also present related results for rational maps on the Riemann sphere.