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Zeros of dynamical zeta functions for hyperbolic quadratic maps

Yuqiu Fu

Vol. 6 (2024), No. 3, 633–656
Abstract

We prove that the dynamical zeta function Z(s) associated to z2 + c with c < 3.75 has essential zero-free strips of size 1 2+ , that is, for every 𝜖 > 0, there exist only finitely many zeros in the strip Re (s) > 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).

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