Zeros of dynamical zeta functions for hyperbolic quadradic maps

Abstract

We prove that the dynamical zeta function $Z(s)$ associated to $z^2+c$ with $c<-3.75$ has essential zero-free strips of size $1/2+$, that is, for every $\epsilon >0$, there exist only finitely many zeros in the strip $\mathrm{Re}(s)>1/2+\epsilon$. We also present some numerical plots of zeros of $Z(s)$ using the method proposed in Jenkinson-Pollicott.

22 pages, 4 figures

References in corpus (2)

• Spectral gaps without the pressure condition
• Fractal uncertainty for transfer operators