Singular perturbation of symbolic flows and poles of the zeta functions. Addendum
type: Item
instance of: scholarly article
title: Singular perturbation of symbolic flows and poles of the zeta functions. Addendum
zbMATH Open document ID: 0771.58039
author: Mitsuru Ikawa
published in: Osaka Journal of Mathematics
publication date: 1993-06-29T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 219868
zbMATH Keywords: scattering matrix
zbMATH Keywords: symbolic flows
zbMATH Keywords: zeta functions
zbMATH Keywords: Lax-Phillips conjecture
reviewed by: William J. Satzer Jr.
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 219868