On deformations of the spectrum of a Finsler--Laplacian that preserve the length spectrum

Abstract

In this article, we show that a Finsler--Laplacian introduced previously can detect changes in the Finsler metric that the marked length spectrum cannot. We also construct examples of non-reversible Finsler metrics in negative curvature such that $4\lambda_1 > h^2$, where $\lambda_1$ is the bottom of the $L^2$-spectrum and $h$ the topological entropy of the flow.