Singular perturbation of symbolic flows and poles of the zeta functions. Addendum (Q1802961)

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.