Singular perturbation of symbolic flows and poles of the zeta functions. Addendum
The author's purpose in studying poles of zeta functions is to show the validity of the modified Lax-Phillips conjecture for obstacles consisting of several small balls. The modified Lax-Phillips conjecture concerns the distribution of the poles of scattering matrices. This paper strengthens the main result of the author's earlier paper [ibid. 27, No. 2, 281-300 (1990; Zbl 0708.58019)] by removing two restrictive assumptions on the configuration of the centers of the balls. The author's new proof of his main result uses the extended Perron- Frobenius theorem applied to each irreducible subsystem in the decomposition of the underlying unperturbed dynamical system.
scientific article; zbMATH DE number 219868