Growth of the Zeta Function for a Quadratic Map and the Dimension of the Julia Set
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Growth and Zeros of the Zeta Function for Hyperbolic Rational Maps
This paper describes new results on the growth and zeros of the Ruelle zeta function for the Julia set of a hyperbolic expanding rational map. It is shown that the zeta function is bounded by exp(CK |s| ) in strips |Re s| ≤ 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)...
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