Growth and Zeros of the Zeta Function for Hyperbolic Rational Maps
| dc.creator | Christianson, Hans | |
| dc.date | 2004-04-30 | |
| dc.date | 2004-05-24 | |
| dc.date.accessioned | 2026-07-07T05:07:49Z | |
| dc.date.available | 2026-07-07T05:07:49Z | |
| dc.description | This paper describes new results on the growth and zeros of the Ruelle zeta function for the Julia set of a hyperbolic rational map. It is shown that the zeta function is bounded by $\exp(C_K |s|^δ)$ in strips $|\Re s| \leq K$, where $δ$ is the dimension of the Julia set. This leads to bounds on the number of zeros in strips (interpreted as the Pollicott-Ruelle resonances of this dynamical system). An upper bound on the number of zeros in polynomial regions $\{|\Re s | \leq |\Im s|^α\}$ is given, followed by weaker lower bound estimates in strips $\{\Re s > -C, |\Im s|\leq r\}$, and logarithmic neighbourhoods $\{|\Re s | \leq ρ\log |\Im s| \}$. Recent numerical work of Strain-Zworski suggests the upper bounds in strips are optimal. | |
| dc.description | 18 pages, 1 figure Expanded Lemma 5.2 and moved to an appendix | |
| dc.identifier | https://arxiv.org/abs/math/0404543 | |
| dc.identifier | http://arxiv.org/abs/math/0404543 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71012 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Complex Variables | |
| dc.subject | 37C30 | |
| dc.title | Growth and Zeros of the Zeta Function for Hyperbolic Rational Maps | |
| dc.type | text |