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- W2951080488 abstract "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 $exp(C_K |s|^{delta})$ in strips $|Re s| leq K$, where $delta$ 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 ${|Re s | leq |Im s|^alpha}$ is given, followed by weaker lower bound estimates in strips ${Re s > -C, |Im s|leq r}$, and logarithmic neighbourhoods ${|Re s | leq rho log |Im s| }$. Recent numerical work of Strain-Zworski suggests the upper bounds in strips are optimal." @default.
- W2951080488 created "2019-06-27" @default.
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- W2951080488 date "2004-04-30" @default.
- W2951080488 modified "2023-09-27" @default.
- W2951080488 title "Growth and Zeros of the Zeta Function for Hyperbolic Rational Maps" @default.
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