Zeros of dynamical zeta functions for hyperbolic quadratic maps

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 $\frac{1}{2} +$ , that is, for every $𝜖 > 0$ , there exist only finitely many zeros in the strip $Re (s) > \frac{1}{2} + 𝜖$ . We also present some numerical plots of zeros of $Z (s)$ based on the method proposed by Jenkinson and Pollicott (Amer. J. Math. 124 (2002), 495–545).

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Keywords

dynamical zeta function, Julia set, Ruelle transfer operator

Mathematical Subject Classification

Primary: 37C30

Secondary: 37F10

Milestones

Received: 26 May 2022

Revised: 14 March 2024

Accepted: 25 April 2024

Published: 1 October 2024

Authors

Yuqiu Fu
Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States

Vol. 6, No. 3, 2024

Yuqiu Fu

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors