A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations

1997 ◽  
Vol 18 (3) ◽  
pp. 653-692 ◽  
Author(s):  
Alan Edelman ◽  
Erik Elmroth ◽  
Bo Kågström
Keyword(s):  
Perturbation Theory ◽  
Geometric Approach ◽  
Matrix Pencils ◽  
Versal Deformations

Perturbation theory of matrix pencils through miniversal deformations

2020 ◽  
Author(s):  
Vyacheslav Futorny ◽  
Tetiana Klymchuk ◽  
Olena Klymenko ◽  
Vladimir V. Sergeichuk ◽  
Nadiya Shvai
Keyword(s):  
Perturbation Theory ◽  
Matrix Pencils

Deformations of Poisson structures on fibered manifolds and adiabatic slow–fast systems

2017 ◽  
Vol 14 (06) ◽  
pp. 1750086 ◽  
Author(s):  
Misael Avendaño-Camacho ◽  
Yury Vorobiev
Keyword(s):  
Perturbation Theory ◽  
Hamiltonian Systems ◽  
Deformation Theory ◽  
Normal Forms ◽  
Geometric Approach ◽  
Fiber Bundles ◽  
Poisson Structures ◽  
Averaging Theorem ◽  
Fibered Manifolds ◽  
Adiabatic Perturbation Theory

In the context of normal forms, we study a class of slow–fast Hamiltonian systems on general Poisson fiber bundles with symmetry. Our geometric approach is motivated by a link between the deformation theory for Poisson structures on fibered manifolds and the adiabatic perturbation theory. We present some normalization results which are based on the averaging theorem for horizontal 2-cocycles on Poisson fiber bundles.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

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