Abstract
I study poles and zeros of zeta functions in one-dimensional maps. Numerical and analytical arguments are given to show that the first pole of one such zeta function is given by the first zero ofanother zeta function: this describes convergence of the calculations of the first zero, which is generally the physically interesting quantity. Some remarks on how these results should generalize to zeta functions of dynamical systems with “pruned” symbolic dynamics and in higher dimensions follow.
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Aurell, E. Convergence of dynamical zeta functions. J Stat Phys 58, 967–995 (1990). https://doi.org/10.1007/BF01026559
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DOI: https://doi.org/10.1007/BF01026559