The Lyapunov spectrum is not always concave

TL;DR

This paper investigates the conditions under which the Lyapunov spectrum of certain dynamical systems is non-concave, providing explicit criteria for linear maps with two branches.

Contribution

It characterizes when the Lyapunov spectrum is non-concave and offers explicit conditions for linear two-branch maps.

Findings

Identifies conditions for non-concave Lyapunov spectra in certain systems

Provides explicit criteria for linear maps with two branches

Enhances understanding of spectrum shape in dynamical systems

Abstract

We characterize one-dimensional compact repellers having nonconcave Lyapunov spectra. For linear maps with two branches we give an explicit condition that characterizes non-concave Lyapunov spectra.