Perturbation theory of observable linear systems

A Linear Perturbation Theory of Inhomogeneous Reionization

We develop an analytic approach to study inhomogeneous reionization on large scales by solving the equations of ionization balance and radiative transfer to first order in perturbations. Given the spatial distribution and spectrum of the ionizing sources, our formalism can be used to predict the large scale power spectra of fluctuations in the abundances of HII, HI and radiation. Our approach a...

Measuring linear operator perturbation from source system observable non-linear response

In Hilbert space, I consider a linear source problem, ill-posed in the zero source critical limit. The solution, flux, depends non-linearly on the linear flux-to-source operator. By perturbation theory and spectral decomposition, I obtain the regularized flux and regularizing control variable, and their responses to any exciting perturbation. The exciting perturbation can be weighed, against th...

A new Approach to the Multi-Objective Control of Linear Singular Perturbation Systems

Perturbation theory for confined systems

We discuss the application of perturbation theory to a system of particles confined in a spherical box. A simple argument shows that the particles behave almost independently in sufficiently strong confinement. We choose the helium atom with a moving nucleus as a particular example and compare results of first order with those for the nucleus clamped at the center of the box. We provide a suita...

Isochronous Systems and Perturbation Theory

This article displays examples of planar isochronous systems and discuss the new techniques found by F. Calogero with these examples. A sufficient condition is found to keep track of some periodic orbits for perturbations of isochronous systems.